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THE    NEW 


TEXT-BOOK    OF    PHYSICS 


AN 


ELEMENTARY  COURSE  IN  NATURAL  PHILOSOPHY 


DESIGNED  FOR  USE  IN 


HIGH    SCHOOLS   AND   ACADEMIES 


BY 

LE  ROY  C.  COOLEY,  PH.D. 

PROFESSOR  OF  PHYSICS  AND  CHEMISTRY  IN  VASSAR  COLLEGE 


IVISON,  BLAKEMAN,   TAYLOR,   AND  COMPANY, 

NEW  YORK  AND  CHICAGO. 


COPYBIGHT,   1868. 


COPTBIQHT,   1880, 

BY  LE  ROY  C.  COOLEY, 


PEEFAOE. 


THE  Text-book  of  Natural  Philosophy,  first  published  in 
1868,  is  now  thoroughly  revised;  and  an  essentially  New 
Text-Book  of  Physics  is  offered  with  the  hope  that  it  will 
prove  to  be  still  more  worthy  of  the  esteem  of  the  friends  of 
sound  learning,  and  still  more  useful  to  the  very  large  num- 
ber of  science-teachers  who  have  so  long  employed  the  older 
book. 

That  which  chiefly  distinguishes  this  New  Text-Book  is  V 
the  prominence  which  it  gives  to  the  principle  of  energy.    ' 
Physics  has  come  to  be  universally  regarded   by  scientists 
as  "the  science  of  matter  and  energy;"   and  I  have  felt,    , 
that,  unless  I  could  fairly  present  the  principle  of  energy  as    / 
the  most  vital  element  of  the  system,  my  work  would   be  / 
altogether  out  of  harmony  with  the  later  views,  and  unworthy  I 
to  be  used  in  the  education  of  the  young,  because  it  would  / 
fail   to   give  the  student  any  adequate  idea  of  the  presentj 
state  of  the  science. 

Various  changes  in  the  arrangement  of  subjects  have  been 
accordingly  made  ;  and  the  doctrine  of  energy,  in  an  element- 
ary form  such  as  it  must  take  in  so  elementaiy  a  work,  will 
be  found  giving  tone  to  all  departments  of  the  course.  The 
first  three  chapters,  treating  of  MATTER  and  MOTION,  will 
abundantly  prepare  the  student  for  the  study  of  ENERGY  in 
the  fourth ;  while,  in  the  remaining  chapters,  he  will  be  able 
to  trace  the  exhibition  of  energy  as  seen  in  the  phenomena 
of  sound,  heat,  light,  electricity,  and  machinery. 

R&4.392 


IV  PREFACE. 

Much  new  matter  has  been  introduced,  as,  for  example,  on 
the  subject  of  electrical  induction,  the  telephone,  the  phono- 
graph, and  other  discoveries  and  applications  which  the  late 
progress  of  science  has  made  fit  subjects  for  an  elementary 
course. 

Among  the  new  features  designed  to  adapt  the  work  to  the 
actual  wants  of  the  class-room,  is  the  Review  at  the  end  of 
every  chapter.  These  reviews  consist  of  Summaries  of  Prin- 
ciples, Summaries  of  Topics,  and  Problems. 

The  summaries  of  principles  are  not  simply  a  re-statement 
of  principles  in  the  order  of  their  previous  discussion :  they 
are  constructed  in  a  way  to  show  these  truths  in  new  rela- 
tions, and  to  supplement  the  synopses  of  the  paragraphs  in 
giving  clear  but  concise  statements  of  the  most  vital  prin- 
ciples of  the  science.  The  summaries  of  topics  follow,  and 
suggest  to  the  mind  all  the  points  in  the  discussion  of  the 
subject  of  every  paragraph.  And  finally  the  problems  tend 
to  make  the  student's  knowledge  more  exact  by  requiring 
him  to  apply  it  mathematically. 

The  References  which  accompany  the  synopsis  of  each 
subject  are  specific,  not  simply  to  a  book  by  title,  but  to 
the  particular  paragraph  of  the  book  where  the  desired  in- 
formation ma}r  be  found  ;  and  not  to  many  and  inaccessible 
authors,  but,  throughout,  to  two,  one  or  the  other  of  which, 
or  both,  may  be  in  the  hands  of  the  teacher  or  pupil. 
Ganot's  Physics  is  selected  because  of  its  excellent  and 
thorough  discussions,  and  Arnott's  because  of  the  appro- 
priate and  interesting  illustrations  in  which  it  abounds. 
These  references  are  designed  for  the  actual  use  of  the 
student  who  is  advanced  enough  and  has  time  to  extend 
his  study  beyond  the  elementary  course  in  this  work,  and 
of  the  teacher  who  desires  to  bring  additional  matter  into 
the  class-room  to  elucidate  or  extend  these  elementary  texts. 

If  circumstances  permit  the   use  of  a  larger  number  of 


PREFACE.  V 

reference-books,  I  would  mention  Deschanel's  Natural  Phi- 
losophy, by  Everett ;  Lardner's  volumes  on  Mechanics  and 
Optics  ;  Silliman's  Physics  ;  Olmstead's  Natural  Philosophy, 
by  Kimball .  Mayer's  works  on  Sound  and  Light ;  Sylvanus 
P.  Thompson's  Electricity  and  Magnetism ;  and  Tyndall's 
several  volumes  on  Sound,  Heat,  Light,  and  Electricity, — 
as  among  those  likely  to  prove  most  generally  useful. 

The  character  of  the  work  is  still  further  indicated  by  the 
following  extracts  from  the  preface  to  the  first  edition :  — 

This  volume  is  designed  to  be  a  text-book  of  natural 
philosophy  suited  to  the  wants  of  high  schools  and  acade- 
mies. 

The  author  believes  that  the  following  features  of  his 
work  adapt  it  to  the  purpose  for  which  it  is  designed  :  — 

1.  It  contains  no  more  than  can  be  mastered  by  average 
classes  in  the  time  usually  given  to  this  science. 

2.  It  presents  a  judicious  selection  of  subjects.     Omitting 
whatever  is  merely  novel  or  amusing,  it  gives  a  plain  and 
concise   discussion   of  elementary  principles,  of  theoretical 
and  practical  value. 

3.  It  is  an  expression  of  modern  theories.     It  recognizes 
the  fact  that  the  spirit  of  a  new  philosophy  pervades  every 
department  of  science,  and  presents  the  doctrines  of  mole- 
cules and  of  molecular  motions,  instead  of  the  old  theory  of 
imponderables,  which  has  been  swept  away.    Carefully  avoid- 
ing whatever  is  yet  only  probable,  it  seizes  upon  what  has 
come  to   be   universally  accepted,  and,  as   far  as   may  be, 
adapts  it  to  the  course   of  elementary  instruction  which  it 
proposes. 

4.  It   is   logical  in  the  arrangement  and  development  of 
subjects.      A   single  chain   of  thought   binds   the   different 
branches  of  the  science  into  one  system  of  related  principles. 

5.  It   is    thoroughly   systematized.      Chapters,    sections, 
paragraphs,    and   topics   have   been   arranged   with   careful 
regard,  on  the  one  hand,  to   the   relation   of  principles  to 


VI  PREFACE. 

each  other,  and,  on  the  other  hand,  to  the  best  methods  of 
conducting  the  exercises  of  the  class-room. 

At  the  beginning  of  each  paragraph  is  a  plain  and  concise 
statement  of  useful  facts  and  principles,  while  the  paragraph 
itself  contains  the  discussion  of  them  by  topics  in  their 
natural  order. 

There  is  an  increasing  number  of  teachers  who  believe 
that  oral  instruction  is  quite  as  important  to  the  pupil  as  the 
study  of  a  text-book.  These  headings  of  the  paragraphs 
are  texts,  which,  taken  together,  give  a  compact  view  of  the 
entire  science,  and  which  will  enable  the  teacher  to  freely 
supplement  the  discussions  of  the  book,  by  experimental  or 
mathematical  proofs.  To  facilitate  this  work  still  further, 
references  have  been  given  to  the  most  accessible  and  relia- 
ble works  wherein  the  subjects  of  the  text  are  more  exhaust- 
ively treated. 

LEll.  C.  C. 
JUNE,  1880. 


CONTENTS. 


CHAPTER   I. 

ON  MATTER  AND  FORCE. 
SECTION.  PAGE. 

I. — NATURAL  PHILOSOPHY  DEFINED 1 

II.  —  ON  MATTER  AND  FORCE 6 

III. — ON  THE  FUNDAMENTAL  IDEAS 16 

IV. —REVIEW                                                    ....  17 


CHAPTER   II. 
ON  THE  THREE  PHYSICAL  FORMS  OF   MATTER. 

I.  —  ON  THE  APPLICATION  OF  THE  FUNDAMENTAL  IDEAS,  20 

II.  —  ON  THE  CHARACTERISTIC  PROPERTIES  OF  SOLIDS     .  21 

III.  —  ON  THE  CHARACTERISTIC  PROPERTIES  OF  LIQUIDS  .  24 

IY.  —  ON  THE  PRESSURE  OF  LIQUIDS 26 

V.  — ON  THE  CHARACTERISTIC  PROPERTIES  OF  GASES      .  43 

YI.  —  ON  ATMOSPHERIC  PRESSURE 48 

VII.  —  ON  "THE  THREE  LAWS"  FOR  GASES         ...  57 

VIII.— REVIEW 62 

CHAPTER   III. 

ON  MOTION. 

I.  —  ON  MOTION  PRODUCED  BY  A  SINGLE  FORCE      .        .  67 

II.  —  ON  MOTION  PRODUCED  BY  MORE  THAN  ONE  FORCE  .  77 

III.  —  ON  THE  MOTION  OF  LIQUIDS 86 

IV. — ON  THE  MOTION  OF  AIR 90 

V.  —  ON  VIBRATION 92 

VI.  —  ON  UNDULATIONS 103 

VII.— REVIEW 109 

vii 


Vlll  CONTENTS. 

CHAPTER   IV. 

ON   ENERGY. 
SECTION.  PAGE. 

I.  —  ON  DEFINITIONS  AND  MEASURES 114 

II.  —  ON  THE  CONSERVATION  OF  ENERGY    .        .        .        .123 

III.  —  ON  THE  RECOGNITION  OF  ENERGY  BY  THE  SENSES  .  126 

IV.—  REVIEW 129 

CHAPTER  V. 

ON  MOLECULAR  ENERGY,  OR  HEAT. 

I.  —  ON  CONDUCTION  AND  CONVECTION       ....  132 

II.  —  ON  THE  EFFECTS  OF  HEAT 135 

III. —REVIEW 146 

CHAPTER   VI. 
ON  UNDULATORY  ENERGY,  OR  SOUND. 

I.  —  ON  TRANSMISSION  AND  REFLECTION  OF  SOUND   .       .  148 

II.  —  ON  MUSICAL  SOUNDS 153 

III.  —  ON  MUSICAL  AND  SENSITIVE  FLAMES  .        .        .        .163 

IV.— REVIEW 167 

CHAPTER  VII. 

ON  RADIANT  ENERGY,  OR  LIGHT. 

I.  —  ON  TRANSMISSION 169 

II.  —  ON  REFLECTION 172 

III.  — ON  REFRACTION 184 

IV.  —  ON  DISPERSION        ........  194 

V. — ON  OPTICAL  INSTRUMENTS    ......  209 

VI.  —  ON  DOUBLE  REFRACTION  AND  POLARIZATION   .        .  216 

VII.— REVIEW 220 

CHAPTER  VIII. 
ON  ELECTRICAL  ENERGY. 

I. — ON  FRICTION AL  ELECTRICITY 224 

II.  —  ON  MAGNETIC  ELECTRICITY 241 

III.  —  ON  DYNAMIC  ELECTRICITY 247 

IV.  —  REVIEW  269 


CONTENTS.  IX 

CHAPTER   IX. 

ON  MACHINERY 

SECTION.  PAGE. 

I. — ON  THE  SIMPLE  MACHINES 274 

II.  —  ON  WATER-POWER 293 

III.  —  ON  THE  STEAM-ENGINE 296 

IV. — REVIEW     ........                ,  300 


PHYSICS, 

OR 

NATURAL    PHILOSOPHY. 


CHAPTER   I. 
ON  MATTER   AND   FORCE. 


SECTION  I.    \  ,  ?Y.  :     *;.  •;  °.;%"  ; 

NATURAL  PHILOSOPHY  DEFINED. 

1.  THE  qualities  of  matter  are  usually  called  its  properties. 
Extension,  Impenetrability,  Indestructibility,  and  Elasticity 
are  examples. 

The  Properties  of  Matter.  —  In  what  respects  is  a  block 
of  granite  so  unlike  a  block  of  wood  ?  The  granite  is  brit- 
tle ;  it  may  be  chipped  with  a  chisel :  the  wood  is  soft ;  it  may 
be  cut  with  a  knife.  The  granite  is  heavy  ;  to  lift  it  may  re- 
quire the  power  of  an  engine :  the  wood  is  much  lighter ; 
perhaps  a  single  arm  is  able  to  move  it.  We  are  thus  able 
to  perceive  a  difference  in  bodies  only  because  there  is  a 
difference  in  the  qualities  they  possess.  These  qualities  are 
called  PROPERTIES. 

Extension.  —  Every  body  of  matter,  however  small,  fills 
a  portion  of  space.  It  is  not  possible  to  think  of  a  body 
which  should  have  no  size.  This  property  of  matter,  by 
virtue  of  which  it  occupies  space,  is  called  EXTENSION. 


2  NATURAL  PHILOSOPHY. 

Measurement  of  Extension.  —  Every  body  of  matter 
must  have  length,  breadth,  and  thickness.  The  amount  of 
space  which  a  body  fills  is  found  by  measuring  these  three 
dimensions.  In  England  and  the  United  States  the  yard  is 
adopted  as  the  unit  of  length.  Feet,  inches,  rods,  and  miles 
are  the  divisions  and  multiples  of  the  yard. 

In  France  and  man}'  other  countries  the  metric  measures 
are  employed,  in  which  the  unit  is  called  the  meter.  The 
meter  is  the  forty-millionth  part  of  that  meridian  of  our  globe 
which  passes  through  Paris.  It  is  equal  to  39.37  inches. 

In  the  metric  system  smaller  units  are  obtained  by  dividing 
the  meter  into  tenths,  hundredths,  and  thousandths ;  and 
larger  ones,  by  multiplying  it  by  ten,  one  hundred,  and  one 
thousand.  The  names  and  values  of  the  smaller  units  are 
'given  on  page  x,  :Fig.  1 . 

•r  Volume*— -  Tlie  amount  of  space  which  a  body  occupies 
cis 'Called  ,its  VOLUME/  For  bodies  of  small  size  the  volume  is 
^measured  In  \3ubic  inches,  or,  by  the  metric  system,  in  cubic 
centimeters.  For  bodies  of  larger  size  a  larger  unit  is  more 
convenient ;  and  their  volumes  are  measured  in  cubic  feet, 
or  cubic  yards,  and  by  the  metric  system,  in  cubic  meters. 

Impenetrability.  —  Not  only  do  all  bodies  occupy  space  : 
every  body  fills  the  space  assigned  it  to  the  exclusion  of  all 
others.  One  body  may  not  be  pushed  into  the  substance  of 
another :  it  can  take  the  place  of  another  only  when  the 
other  has  been  thrust  away.  When,  for  example,  a  nail  is 
driven  into  wood,  it  pushes  the  particles  of  wood  out  of  its 
way  ;  and,  when  the  hand  is  plunged  into  water,  the  water  is 
thrust  aside  to  give  it  place.  This  property  of  matter,  by 
virtue  of  which  no  two  bodies  can  fill  the  same  space  at  the 
same  time,  is  called  IMPENETRABILITY. 

Indestructibility.  —  A  piece  of  gold  may  be  cut  into 
parts  so  small  as  to  be  almost  invisible.  It  may  be  dissolved 
by  acids,  and  made  to  disappear  ;  or  by  intense  heat  it  may  be 
changed  into  thin  vapor,  and  hid  in  the  air.  After  all  these 
changes  have  been  wrought  upon  the  gold,  its  particles  may 


NATtJRAL  PHILOSOPHY.  8 

be  again  collected  to  form  a  mass  like  the  original  one  with- 
out the  slightest  diminution  in  weight.  Amid  all  the  changes 
which  we  witness  in  the  forms  and  qualities  of  bodies,  not  a 
single  atom  is  destro}red.  This  property  of  matter,  by  virtue 
of  which  no  particle  can  be  destroyed,  is  called  INDESTRUCTI- 
BILITY. 

Elasticity.  —  When  an  India-rubber  ball  is  pressed  in  the 
hand,  it  is  made  smaller ;  but,  the  moment  the  pressure  is 
removed,  the  ball  springs  back  to  its  original  size.  The 
same  quality  is  possessed  in  various  degrees  by  all  bodies. 
In  such  as  lead  and  clay  it  is  very  slight,  yet  a  ball  made  of 
either  of  these  substances  will  spring  back  after  having  been 
for  a  moment  compressed.  On  the  other  hand,  an  ivory  ball, 
when  let  fall  upon  a  marble  slab,  rebounds  nearly  to  the 
height  from  which  it  fell,  showing  that  the  power  of  restitu- 
tion is,  in  this  case,  almost  equal  to  the  force  of  compression. 
Tliis  property  of  matter,  by  virtue  of  which  it  restores  itself 
to  its  former  condition  after  having  yielded  to  some  force,  is 
called  ELASTICITY. 

Are  all  Bodies  elastic?  —  This  property  of  matter  is 
possessed  by  all  bodies.  Some  are  very  slightly  elastic  ;  such 
are  lead  and  clay.  Glass,  although  very  brittle,  is  highly 
elastic.  A  glass  ball  will  rebound  from  a  marble  slab  almost 
as  well  as  one  of  ivory.  Steel  is  likewise  hard  and  brittle  ;  yet 
the  Damascus  sword,  which  was  made  of  steel,  could  be  bent 
double  without  breaking. 

But,  should  we  attempt  to  describe  all  the  properties  of 
matter  in  detail,  the  time  given  to  the  study  of  our  science 
would  be  filled  with  little  else.  The  success  of  a  student  of 
nature  depends  largely  upon  his  power  to  classify  phenomena, 
and  to  study  them  in  groups. 

2.  All  the  properties  of  matter  may  be  grouped  in  two 
divisions,  viz. :  Physical  Properties,  of  which  malleability 
and  ductility  are  examples  ;  and  Chemical  Properties,  such 
as  combustibility  and  explosjbility. 


4  NATURAL   PHILOSOPHY. 

I. -PHYSICAL   PROPERTIES. 

Malleability.  —  Many  of  the  metals  may  be  reduced  to 
thin  plates,  or  leaves,  by  hammering  them.  Zinc  is  a  famil- 
iar illustration,  sheets  of  this  metal  being  often  placed  under 
stoves  to  protect  the  floor  from  heat.  This  property  is  called 
MALLEABILITY.  Gold  is  eminently  malleable :  it  may  be  beaten 
into  leaves  so  thin  that  a  pile  of  eighteen  hundred  of  them 
would  be  no  thicker  than  a  sheet  of  common  paper. 

Ductility.  —  Many  substances  ma}'  be  also  drawn  into 
wire.  Iron,  copper,  and  brass  wires  are  sufficiently  familiar. 
The  peculiar  property  by  virtue  of  which  the}'  may  be  drawn 
into  wire  is  called  DUCTILITY.  Glass,  when  heated  to  a  bright 
red  heat,  is  remarkably  ductile.  If  a  point  pulled  out  from 
the  mass  be  fastened  to  the  circumference  of  a  turning  wheel, 
a  uniform  thread  as  fine  as  the  finest  silk  ma}'  be  wound  at  the 
rate  of  a  thousand  yards  an  hour. 

Physical  Properties.  —  Now  fix  the  attention  upon  the 
fact  that  the  wonderful  malleability  of  gold  and  the  surprising 
ductility  of  glass  are  shown  without  any  change  in  the  nature 
of  these  substances.  The  gold  is  the  same  material  in  the 
form  of  leaf  as  it  was  before  it  manifested  its  malleability. 
The  glass  in  the  form  of  thread  is  the  identical  substance 
which,  by  being  drawn,  manifested  its  ductility. 

All  properties  which,  like  these,  a  body  may  manifest  with- 
out undergoing  any  change  in  its  nature,  are  called  PHYSICAL 
PROPERTIES. 

If  now  we  examine  those  properties  described  in  the  early 
part  of  this  section,  we  shall  find  them  all  to  belong  to  this 
group.  Extension,  Impenetrability,  and  the  rest,  are  proper- 
ties which  a  body  may  show  without  any  change  in  its  nature. 

II.  —  CHEMICAL  PROPERTIES. 

Chemical  Properties.  —  Wood,  by  burning,  shows  that  it 
is  combustible.  No  substance  can  manifest  the  property  of 
combustibility  except  by  actually  taking  fire  ;  and  when  it 
burns  it  changes  to  something  else. 


NATURAL  PHILOSOPHY.  5 

Who,  not  already  familiar  with  gunpowder,  would  suspect  it 
to  be  so  violently  explosive  ?  It  can  show  that  it  is  explosive 
only  by  ceasing  to  be  gunpowder,  and  becoming  a  mass  of 
vapor.  Properties  like  these,  which  a  body  can  not  manifest 
without  changing  its  nature,  are  called  CHEMICAL  PROPERTIES. 

This  classification  of  properties  wTill  help  us  to  define  accu- 
rately the  science  whose  elements  we  are  beginning  to  study. 

3.  Natural  Philosophy,  or  Physics  as  it  is  now  more  gen- 
erally called,  is  the  science  which  treats  of  the  physical  prop- 
erties of  matter,  and  of  those  phenomena  in  which  there  is 
no  change  in  the  nature  of  bodies. 

Illustrations.  —  If  now  we  look  out  upon  the  phenomena 
which  nature  presents,  and  will  apply  the  test  furnished  by 
this  definition,  we  may  select,  from  among  the  multitude,  those 
which  it  is  the  province  of  this  science  to  explain.  Thus,  for 
example,  we  see  the  vapors  rise ;  we  see  the  raindrops  fall ; 
we  listen  with  delight  to  the  harmonies  of  music,  and  derive 
exquisite  pleasure  from  the  colors  of  the  rainbow.  In  these 
phenomena,  and  in  numerous  others  easily  recognized  by  an 
attentive  mind,  we  can  detect  changes  in  the  form  and  place 
of  bodies,  but  none  whatever  in  their  nature.  We  therefore 
expect  to  learn  the  explanation  of  them  in  the  study  of 
physics.  But  if  we  regard  the  more  quiet  yet  not  less  impos- 
ing phenomena  of  the  seasons,  we  may  discover  a  multitude 
whose  discussion  is,  by  the  definition,  excluded  from  this 
science.  The  young  verdure  of  the  springtime  changes  at 
length  to  the  matured  foliage  and  ripening  grains  of  summer. 
The  fruits  and  hues  of  autumn,  more  somber  except  where 
enlivened  by  the  richly  colored  ripening  leaves  of  the  maple 
or  the  oak,  soon  afterward  appear,  only  to  be  in  turn  dis- 
placed by  the  snows  of  winter.  These  events  are  brought 
about  by  changes  gradually  taking  place  in  the  nature  of 
substances  ;  and  the  explanation  of  all  such  phenomena  must 
be  reserved  for  the  science  of  chemistry. 


6  NATURAL  PHILOSOPHY. 

SECTION  II. 

ON  MATTER  AND  FORCE. 

4.  Matter,  with  respect  to  its  Divisibility,  may  be  consid- 
ered either  as  Masses,  Molecules,  or  Atoms.  (O.  2,  3  ;  A.  1, 
2,  7-10.1) 

Divisibility.  —  Every  body  of  matter  may  be  cut  or 
broken  into  pieces.  This  quality  or  property  of  matter  is 
called  DIVISIBILITY. 

Examples  of  minute  Division.  —  There  are  bodies  all 
around  us  so  small  that  we  can  not  see  them.  They  are  in 
the  air  we  breathe,  and  the  water  we  drink ;  some  of  them 
are  so  minute  that  only  the  most  powerful  microscope  can 
enable  us  to  discover  them.  Common  salt  can  be  detected 
by  chemical  means  in  the  air,  even  at  great  distances  from 
the  sea,  and  when  the  air  is  perfectly  transparent. 

There  are  living  creatures  so  small  that  a  million  indi- 
viduals together  would  be  no  larger  than  a  mustard-seed. 
Yet  each  one  must  be  made  up  of  parts,  else  it  could  not 
move  about,  and  take  its  food,  as  all  of  them  can  do. 

A  grain  of  cochineal  dissolved  in  water  will  impart  a  dis- 
tinct color  to  a  whole  gallon.  That  it  may  do  this,  it  is  esti- 
mated that  the  grain  must  be  divided  into  not  less  than  six 
million  pieces. 

Masses.  —  A  mass  is  any  separate  portion  of  matter, 
whether  large  or  small.  A  block  of  marble  or  a  particle  of 
the  dust  into  which  it  may  be  crushed,  the  grain  of  cochineal 
or  one  of  its  six  million  pieces,  is  a  MASS. 

Molecules.  —  But  there  is  a  limit  bej'ond  which  a  mass 
can  not  be  divided  without  changing  the  nature  of  its  sub- 

1  Books  of  reference  are  indicated  as  follows :  {?.,  Ganot's  Physics,  by  Atkinson, 
8th  ed.,  1877 ;  A.,  Arnott's  Physics,  by  Bain  and  Taylor,  7th  ed.,  1877.  Numbers  refer 
to  paragraphs,  not  to  pages.  The  dash  between  two  numbers  means  that  all  the 
paragraphs  between  are  included :  e.g.,  "  7-10  "  refers  to  paragraphs  7,  8,  9,  and  10. 


NATURAL  PHILOSOPHY.  7 

stance.  A  block  of  ice,  for  example,  may  be  crushed  until 
its  particles  are  like  the  finest  dust,  but,  if  its  temperature  be 
kept  low  enough  while  it  is  being  crushed,  every  particle  of 
the  ice-powder  will  still  be  a  block  of  ice.  By  applying  heat, 
the  little  block  is  first  melted,  and  then  changed  to  steam, 
which  shows  that  it  was  composed  of  innumerable  smaller 
pieces.  How  minute  must  be  the  particles  thus  made  abso- 
lutely invisible  !  Yet  each  one  is  a  fragment  of  the  original 
block  of  ice.  The  heat  has  not  changed  their  nature.  The 
identical  particles  which  make  up  the  steam  composed  the 
drop  of  water  and  the  little  piece  of  ice.  But  it  is  thought 
that  these  particles  can  not  be  divided  without  changing 
their  nature,  and  they  are  called  MOLECULES. 

A  molecule  is  a  particle  of  matter  which  can  not  be  divided 
without  changing  its  chemical  character. 

All  bodies  are  made  up  of  molecules.  The  size  of  a  body 
depends  upon  their  number ;  its  shape,  upon  their  arrange- 
ment. 

Atoms.  —  If  the  molecules  are  broken  or  divided,  the 
character  of  the  substance  is  changed.  Let  steam,  for  ex- 
ample, be  passed  into  a  red-hot  gun-barrel :  that  which  issues 
from  the  other  end  is  not  steam,  but  hydrogen  gas,  while 
another  gas,  oxygen,  combines  with  the  iron  of  the  gun- 
barrel.  The  molecules  of  steam  are  broken  into  pieces,  but 
the  substance  is  no  longer  steam.  These  smaller  parts  are 
particles  of  hydrogen  and  oxygen. 

The  chemist  finds  that  there  are  two  pieces  of  hydrogen 
and  one  of  oxygen  obtained  whenever  a  molecule  of  water 
is  divided.  But  no  way  has  yet  been  found  to  carry  the 
division  any  further;  and  these,  the  smallest  of  all  frag- 
ments into  which  matter  can  be  divided,  are  called  ATOMS. 
By  combining  trigitbflr,  atoms  form  molecules. 

An  atom  is  the  smallest  portion  of  matter  that  can  enter 
into  combination. 

What  is  Inertia  ?  —  Masses  of  matter  have  no  power  to 
move  themselves,  nor  to  stop  themselves  when  once  in  motion. 


8  NATURAL  PHILOSOPHY. 

A  heavy  wheel  requires  force  to  put  it  in  motion,  or  when 
in  motion  it  requires  force  to  stop  it.  It  has  no  power  to 
change  its  own  condition.  At  rest,  it  would  rest  forever  if 
left  to  itself;  or  once  in  motion  it  would  forever  move,  unless 
acted  upon  by  some  force  beyond  itself. 

Molecules  and  atoms  also  are  powerless  to  change  their 
own  condition.  It  is  believed  that  the  molecules  of  every 
body  are  in  motion  always,  but  no  molecule  can  in  any  way 
change  its  own  velocity  or  direction.  Inertia  is  the  property 
of  matter  which  does  not  allow  a  body  to  change  its  own  con- 
dition of  rest  or  motion. 

5.  Forces  are  either  attractive  or  repellent.     (6r.  26.) 

Force.  —  Bodies  are  sometimes  in  motion,  and  sometimes 
at  rest.  Their  motion  is  at  one  time  swift,  at  another  slow. 
Now,  inertia  prevents  any  body  from  causing  these  changes 
in  itself,  and  we  must  attribute  them  to  the  influence  of 
other  bodies.  Whatever  this  influence  may  be,  it  is  called 
FORCE. 

Force  is  the  name  given  to  the  influence  which  tends  to  pro- 
duce or  diminish  or  in  any  way  change  the  motion  of  bodies. 

Attraction.  —  When  a  body  is  not  supported  it  falls  to 
the  ground.  This  familiar  event  illustrates  the  tendency  of 
bodies  to  approach  each  other.  Moreover,  we  have  seen 
that  bodies  are  composed  of  molecules,  so  small  that  the 
most  powerful  microscope  can  not  reveal  them,  yet  we  must 
think  of  each  as  a  separate  body  as  truly  as  though  the  eye 
could  measure  its  diameter.  Now,  by  what  influence  are 
they  held  together?  It  is  doubtless  the  same  invisible  force 
by  which  a  body  is  drawn  to  the  earth  when  not  supported. 
It  is  a  fact  that  all  bodies,  however  large  or  small,  have  a 
tendency  to  approach  each  other.  The  force  which  causes 
this  tendency  is  called  ATTRACTION. 

Repulsion.  —  If  a  ball  of  India-rubber  be  pressed  in  the 
hand,  it  is  made  smaller;  its  molecules  are  brought  nearer 
together.  When  the  pressure  is  removed,  they  instantly 


NATURAL   PHILOSOPHY. 


9 


spring  to  their  former  position.     While  springing  back  the 
molecules  are  evidently  being  thrust  away  from  each  other. 

Or  try  the  following  experiment  (Fig.  2)  :  Suspend  a 
pith-ball,  or  a  little  ball  of  cotton,  by  a  fine  silk  thread : 
briskly  rub  a  warm  dry  strip  of  glass  with  a  woolen  cloth : 
bring  the  ball  and  glass  together  for  a  moment,  after  which 
it  will  be  found  that  the  ball  will  fly  away  from  the  glass, 
and  show  so  strong  an  aversion  to  it  that  they  can  not  be 
brought  together.  That  which  keeps  them  apart  is  called 
REPULSION. 


Fig 


An  influence  under  which  bodies  tend  to  separate  is  called 
REPULSION. 

Molecular  Repulsion.  —  The  action  of  repulsion  among 
molecules  is  more  universal  than  among  masses.  It  is  illus- 
trated by  man}'  familiar  facts.  If,  for  example,  a  bladder  be 
filled  with  cold  air,  and  then  heated,  it  will  burst.  Repul- 
sion drives  the  molecules  of  air  apart,  and  pushes  them 
through  the  bladder.  When  a  drop  of  water  is  heated  it 
becomes  steam,  and  fills  a  space  about  seventeen  hundred 
times  larger  than  before. 


10  NATURAL  PHILOSOPHY. 

Notice  that  in  these  examples  the  separation  of  the  mole- 
cules is  due  to  heat.  It  is  believed  that  all  molecular  repulsion 
is  the  same  influence  as  that  which  shoivs  itself  as  HEAT. 

The  Forces  of  Mature.  —  We  speak  of  the  forces  of 
nature,  and  call  them  wind,  water,  gravitation.  This  is  well, 
because  these  names  have  been  given  to  familiar  forms  of 
force.  We  will  continue  to  use  these  terms :  at  the  same 
time,  let  us  do  justice  to  the  simplicity  of  God's  stupendous 
works,  by  remembering  that  all  the  forces  of  nature  are 
only  different  manifestations  of  attraction  and  repulsion. 

6.  Attraction  receives  different  names  according  to  the  cir- 
cumstances under  which  it  acts.  Gravitation,  Cohesion,  Ad- 
hesion, and  Chemism  are  its  most  common  forms.  (G.  84-87  ; 
A.  18-28,  86,  87.) 

I.  —  GRAVITATION. 

Gravitation  denned.  —  Gravitation  is  that  form  of  at- 
traction which  is  exerted  upon  all  bodies,  and  throughout  all 
distances.  The  leaf,  the  fruit,  the  snow-flake,  fall  to  the 
ground  because  they  are  attracted  thither  by  gravitation. 
They  press  upon  its  surface  because  the  same  force  continues 
to  act  after  they  reach  the  earth.  No  distance  can  outreach 
it,  for  it  is  the  bond  which  holds  the  heavenly  bodies  in  their 
orbits.  Nor  can  an}^  substance  cut  it  off,  or  even  diminish 
its  action ;  for,  if  the  earth  should  come  between  the  sun  and 
moon,  these  two  bodies  would  still  attract  each  other  with 
the  same  degree  of  force. 

Governed  by  two  Laws.  —  The  intensit}T  of  gravitation 
between  bodies  depends  on  two  things, — the  quantity  of 
matter  contained  in  them,  and  the  distance  between  their 
centers.  The  "law  of  gravitation,"  discovered  by  Newton, 
consists  of  two  parts  which  express  these  two  relations.  We 
may  study  them  as  two  laws. 

The  First  Law  of  Gravitation.  —  Suppose  two  bodies, 
one  containing  twice  as  much  matter  as  the  other,  to  attract 


NATURAL  PHILOSOPHY.  11 

a  third.  The  force  exerted  by  the  first  will  be  twice  as  great 
as  that  by  the  other.  If  one  body  weighs  nine  tons  and 
another  three  tons,  then  a  third  body  equally  distant  from 
them  will  receive  three  times  as  much  attraction  from  the 
first  as  from  the  second.  These  facts  illustrate  the  law  that 
the  force  of  gravitation  varies  directly  as  the  quantity  of 
matter  exerting  it. 

The  Second  Law  of  Gravitation.  —  Suppose  a  body  to 
be  twice  as  far  from  the  center,  or  source  of  attraction,  at  one 
time  as  at  another.  In  the  first  position,  the  attraction  will 
be  only  one-fourth  as  strong  as  in  the  second.  If  the  dis- 
tance be  three  times  as  great,  the  force  will  be  one-ninth  as 
strong.  If  two  distances  are  as  3  :  4,  the  attractions  will  be 
to  each  other  as  16:  9.  These  facts  illustrate  the  law  that 
the  force  of  gravitation  varies  inversely  as  the  square  of  the 
distance  through  which  it  acts. 

Weight.  —  The  weight  of  a  body  is  the  downward  press- 
ure which  it  is  able  to  exert.  It  is  due  to  the  attraction  of 
gravitation  exerted  by  the  earth.  Weight  must  therefore 
increase  or  diminish  in  exact  accordance  with  the  laws  of 
gravitation. 

Is  proportional  to  the  Quantity  of  Matter.  —  Accord- 
ing to  the  first  law,  a  double  quantity  of  matter  is  attracted 
by  the  earth  with  a  double  force,  and  it  therefore  weighs  twice 
as  much.  For  the  same  reason,  if  the  quantities  of  matter 
in  two  bodies  are  as  1  :  4,  their  weights  must  also  be  as  1  :  4. 
That  is  :  the  weights  of  bodies  are  proportional  to  the  quanti- 
ties of  matter  in  them. 

And  inversely  proportional  to  the  Square  of  the  Dis- 
tance from  the  Earth's  Center. — According  to  the  second 
law,  the  greater  the  distance  from  the  earth,  the  less  will  a 
body  weigh.  Now,  distance  from  the  earth  is  measured  from 
its  center.  When  on  the  surface  of  the  earth,  a  body  is  four 
thousand  miles  from  the  center  ;  suppose  it  were  possible  to 
carry  the  body  to  a  height  of  four  thousand  miles  above  the 
surface,  its  distance  from  the  center  would  be  doubled,  and 
its  weight  would  be  reduced  to  one-fourth. 


12  NATURAL   PHILOSOPHY.     • 

Not  limited  to  Bodies  on  the  Earth.  —  Since  the  laws 
of  gravitation  are  universal,  a  body  on  the  moon  or  an}'  other 
heavenly  body  has  weight. 

Not  the  same  as  Mass.  —  By  mass,  we  mean  the  quantity 
of  matter  in  a  bod}r.  We  speak  of  the  body  itself  as  a  mass 
to  distinguish  it  from  molecules  and  atoms ;  but  the  mass 
of  a  bod}7  is  the  quantity  of  matter  it  contains. 

A  body  on  the  moon,  for  example,  would  have  the  same 
quantity  of  matter  in  it  as  if  upon  the  earth.  Yet  the  moon 
could  exert  much  less  attraction  than  the  earth,  and  hence 
the  weight  of  the  bod}7  would  be  less.  Mass  is  the  quantity 
of  matter  in  a  body ;  weight  is  the  force  of  attraction  ex- 
erted on  it.  The  mass  of  a  bod}T  is  everywhere  the  same  ;  its 
weight  is  different  at  different  places.  Bat  at  any  one  place 
the  weights  of  all  bodies  are  proportional  to  their  masses; 
and  for  this  reason  we  can  compare  the  quantities  of  matter 
in  bodies  b}r  weighing  them. 

II.  —  COHESION. 

Cohesion  defined.  —  Cohesive  attraction  holds  the  mole- 
cules of  a  body  together,  and  enables  it  to  keep  its  form  and 
size.  A  cubical  block  of  wood  remains  a  cube  only  because 
its  molecules  are  held  together  by  this  force.  Were  it  not 
for  its  action,  all  bodies  would  at  once  dissolve  into  their 
ultimate  molecules,  and  vanish. 

COHESION  is  that  form  of  attraction  which  acts  between  the 
molecules  of  the  same  body. 

Its  Power  is  very  great.  —  The  strength  of  cohesion  is 
often  very  great.  The  molecules  of  a  piece  of  iron  are  so 
strongly  bound  by  it,  that  a  weight  of  five  hundred  pounds 
may  be  lifted  by  means  of  a  wire  one-tenth  of  an  inch  in 
diameter.  Even  a  strip  of  paper  is  not  easily  broken  b}T  a 
force  acting  exactly  in  the  direction  of  its  length. 

But  it  acts  through  Insensible  Distances.  —  The  dis- 
tance through  which  cohesion  can  act  is  quite  too  small  to 
be  measured.  Let  the  parts  of  a  body  be  separated,  and  the 
strength  of  the  giant  is  gone. 


NATURAL   PHILOSOPHY.  13 

When  a  body  is  broken,  its  parts  can  be  made  to  cohere 
again  only  with  great  difficulty.  In  a  few  soft  bodies,  like 
wax,  a  slight  pressure  will  force  the  molecules  near  enough 
together  for  cohesion  to  take  hold  of  them ;  in  others,  the 
pressure  required  is  much  greater ;  while  in  the  majority  of 
substances  it  is  so  great  as  to  be  practically  impossible. 

Welding-.  —  The  smith  unites  two  pieces  of  iron  by  weld- 
ing. He  softens  the  iron  by  heat,  then  puts  the  two  pieces 
together,  and  unites  them  by  the  heavy  blows  of  his  sledge. 
All  that  he  does  is  simply  to  push  the  yielding  molecules 
of  the  two  pieces  of  iron  into  very  close  contact ;  this  done, 
cohesion  grasps  them,  and  the  two  pieces  become  one. 

III.— ADHESION. 

Adhesion  defined If  the  hand  be  plunged  into  water, 

it  comes  out  covered  with  a  thin  film  of  the  fluid ;  it  may  be 
immersed  in  alcohol  with  the  same  effect.  When  one  writes 
upon  the  blackboard,  he  leaves  fine  particles  of  the  crayon 
clinging  to  the  surface  of  the  board. 

In  all  such  cases  we  notice  that  there  is  an  attraction 
between  particles  of  different  kinds  of  matter.  Attraction 
between  particles  of  unlike  kinds  is  called  ADHESION. 

By  what  Experiment  may 
we  illustrate  it?  — A  very  pret- 
ty experiment  is  shown  in  Fig.  3. 
It  illustrates  the  adhesion  between 
water  and  brass.  A  round  plate 
of  brass,  having  a  handle  fastened 
to  its  center,  is  laid  flat  upon  the 
surface  of  water,  and  then  slowly 
and  gently  lifted.  The  water  un- 
der it  is  also  lifted  a  little,  as  the 
picture  shows  it  to  be. 

You  can  use  a  plate  of  wood  or  of  glas.  in  the  same 
way. 

Adhesion  of  Solids  to  Solids.  —  The  value  of  glue  and 


14 


NATURAL  PHILOSOPHY. 


cement  is  due  to  the  powerful  adhesion  which  acts  between 
them  and  the  surfaces  of  solid  bodies  which  they  bind  to- 
gether. 

Adhesion  of  Liquids  to  Solids.  —  If  small  glass  tubes 
be  inserted  in  a  vessel  of  water,  it  will  be  seen  that  the  fluid 
instantly  springs  upward,  and  remains  at  rest  in  the  tubes 
considerably  above  its  general  level.  (See  Fig.  4.)  Along 

the  outside  surface  of  the  tubes 
the  water  also  climbs  to  a  little 
height. 

If  tubes  be  inserted  in  a 
vessel  of  mercury,  this  fluid 
will  be  pushed  down.  (Fig. 
5.)  The  mercury  inside  the 


Fig.  4. 


Fig.  5. 


tubes  will  be  considerably  be- 
low the  general  level,  while  the  fluid  against  the  outside  is 
also  depressed.  Here  are  two  well-marked  cases  of  the 
action  of  adhesion. 

Whenever  a  piece  of  glass  is  plunged  into  water  it  comes 
out  wet,  but  when  plunged  into  mercury  it  comes  out  as  free 
from  the  liquid  as  when  it  entered  ;  and  by  repeated  experi- 
ments it  is  shown  that  all  liquids  which  will  wet  the  sides  of 
the  tube  will  be  lifted,  while  those  which  will  not  will  be 
pushed  down. 

Capillarity.  —  The  elevation  or  depression  of  fluids  in 
small  tubes  is  called  CAPILLARITY.  The  attraction  causing  it 
is,  however,  nothing  different  from  adhesion. 

It  causes  Liquids  to  penetrate  Porous  Solids.  —  An 
eas3r  experiment  strikingly  illustrates  this  action.  Take  a 
common  bottle,  eight  or  ten  inches  high,  and  wrap  it  in  a 
sheet  of  white  blotting-paper,  whose  edges  must  be  secured 
by  a  bit  of  wax.  Place  the  bottle,  now  prepared,  upon  a 
dinner-plate.  Pour  water  upon  the  plate  to  cover  the  lower 
edge  of  the  paper ;  and  immediately  the  fluid  will  be  seen 
rapidly  climbing  the  sides  of  the  bottle,  which  it  will  not 
cease  to  do  until  it  has  reached  the  top. 


NATURAL  PHILOSOPHY.  15 

Explanation.  —  The  rise  of  the  water  is  due  to  the  at- 
traction between  its  particles  and  those  of  the  paper  and 
glass.  This  force,  acting  downward  from  each  particle  of 
the  paper  through  the  definite  but  imperceptible  distance  to 
the  one  below  it,  lifts  a  particle  of  water.  The  next  particle 
of  paper  above  then  lifts  it  higher.  Indeed,  the  successive 
particles  of  paper  upward  are  the  successive  steps  of  a  lad- 
der, up  which  the  water  is  impelled  by  capillary  force. 

Familiar  Examples.  —  Numerous  familiar  facts  are  ex- 
plained by  this  experiment.  Oil  is  carried  up  the  lamp-wick 
to  supply  the  flame  with  fuel.  Ity  a  similar  action,  water 
is  distributed  through  loose  soils  to  keep  them  moist  and 
fertile.  So,  too,  in  a  great  degree,  the  sap  of  plants  and 
trees  is  carried  to  their  summits  ;  and  even  in  the  animal 
system  the  circulation  of  blood  through  the  minute  blood- 
vessels is  materially  aided  by  capillary  action. 

Tlie  Law. — In  Fig.  4,  the  water  is  represented  as  being 
lifted  to  different  heights  in  the  tubes.  The  height  to  which 
any  fluid  rises  depends  upon  the  size  of  the  tube.  If  the 
diameter  of  one  tube  be  just  one-half  that  of  another,  water 
will  invariably  rise  in  it  twice  as  far.  If  the  diameters  of 
two  tubes  have  the  ratio  of  4:3,  then  the  water  will  rise  in 
them  to  heights  whose  ratio  is  3:4.  These  facts  illustrate 
the  law  that  the  heights  to  which  a  liquid  rises  in  different 
tubes  of  the  same  material  are  inversely  proportional  to  the 
diameters  of  the  tubes. 

A  tube  one-hundredth  of  an  inch  in  diameter  will  lift 
water  to  a  height  of  about  four  inches. 

IV .  —  CHEMISM. 

Chemism  defined.  —  When  coal  burns,  the  carbon  of 
which  it  is  composed  combines  with  the  oxygen  of  the  air. 
They  form  a  new  substance  called  in  chemistry  carbonic  di- 
oxide. The  properties  of  carbonic  dioxide  are  very  unlike 
those  of  either  coal  or  oxygen. 

This  action  occurs  among  the  atoms  of  coal  and  oxygen. 


16  NATURAL   PHILOSOPHY. 

Under  the  influence  of  the  heat  these  unlike  atoms  are  drawn 
together,  and  then  so  firmly  held  that  they  seem  to  be  one 
body.  They  form  molecules  of  carbonic  dioxide. 

The  attraction  which  holds  the  atoms  together  in  a  mole- 
cule is  called  CHEMISM.  Chemical  affinity  is  another  and  an 
older  name  for  it. 


SECTION   III. 
ON  THE  FUNDAMENTAL   IDEAS. 

7.  The  fundamental  ideas  in  regard  to  matter  and  force 
are  suggested  by  the  words,  Molecules,  Inertia,  Attraction, 
and  Repulsion. 

These  terms  have  been  already  defined;  but  they  may 
suggest  to  the  mind  much  more  of  what  is  believed  about 
the  minute  constitution  of  matter  than  their  definitions  con- 
tain. 

Principle  suggested  by  the  Term  Molecule.  —  Every 
body  of  matter  is  made  up  of  a  multitude  of  little  particles, 
which  do  not  touch  each  other,  which  are  forever  in  motion, 
and  which  can  not  be  divided  without  changing  their  nature. 

Principle  suggested  by  the  Term  Inertia.  —  No  body 
of  matter  —  a  mass,  a  molecule,  nor  an  atom  —  has  power  to 
change  its  own  condition  of  rest  or  motion. 

Principle  suggested  by  the  Term  Attraction.  —  All 
bodies  of  matter  —  masses,  molecules,  and  atoms — tend  to 
approach  one  another. 

Principle  suggested  by  the  Term  Repulsion.  —  There 
is  also  an  influence  under  which  molecules  tend  to  separate, 
and  which  forbids  their  actual  contact  in  a  body. 

Of  these  four  Ideas.  —  These  four  ideas  may  be  so  com- 
bined as  to  yield  the  explanation  of  almost  all  the  phenom- 
ena which  appear  in  nature.  A  great  city,  with  all  its 
various  forms  of  architecture  and  machinery,  is  built  of  a 


NATURAL   PHILOSOPHY.  17 

few  familiar  substances,  such  as  wood  and  iron  and  stone. 
This  fact  may  excite  our  admiration  of  the  intelligence  and 
skill  of  man.  What,  then,  must  be  our  feelings  when  we 
discover  that  these  four  simple  ideas  are  the  elements  out  of 
which  the  sublime  fabric  of  the  universe  has  arisen !  The 
whole  system  of  material  things  is  simple  and  orderly,  dis- 
playing the  infinite  knowledge,  power,  and  skill  of  a  divine 
Architect. 


SECTION  IV. 

REVIEW. 
I.— SUMMARY   OF  PRINCIPLES. 

In  the  foregoing  chapter  we  have  found  that :  — 

All  properties  of  matter  are  either  physical  or  chemical. 

Physics  or  Natural  Philosophy  is  the  science  which  treats 
of  the  physical  properties  of  matter,  and  of  those  phenomena 
in  which  there  is  no  change  in  the  nature  of  substances. 

Matter  may  be  considered  as  consisting  of  masses,  mole* 
cules,  and  atoms. 

Forces  are  either  attractive  or  repellent. 

Attraction  is  called 

Gravitation,  when  it  acts  between  masses  ; 

Cohesion  or  adhesion,  when  it  acts  between  molecules ; 

Chemism,  when  it  acts  between  atoms. 

The  force  of  gravitation  varies  directly  as  the  quantity  of 
matter  exerting  it,  and  inversely  as  the  square  of  the  dis- 
tance through  which  it  acts. 

Volume  is  the  space  occupied  by  a  body. 

Mass  is  the  quantity  of  matter  in  a. body. 

Weight  is  the  pressure  of  a  body  downward,  caused  by 
the  attraction  of  the  earth. 

The  fundamental  ideas  of  matter  and  force  are  suggested 
by  the  words,  Molecule,  Inertia,  Attraction,  and  Repul- 
sion. 


18  NATURAL  PHILOSOPHY. 

II. —SUMMARY   OF  TOPICS. 

1.  Properties  of  matter.  —  Extension.  —  Impenetrability. 

—  Indestructibility.  —  Elasticity. 

2.  Malleability.  --  Ductility.  —  Definition     of    physical 
properties.  —  Definition  of  chemical  properties. 

3.  Definition  of  Physics.  — Illustrations. 

4.  Divisibility.  —  Examples.  —  Masses.  —  Molecules.  — 
Atoms.  —  Inertia. 

5.  Force.  —  Attraction.  —  Repulsion.  —  Molecular   repul- 
sion. 

6.  Gravitation  described.  —  Governed   by   two  laws.  — 
The   first   law.  —  The   second   law.  —  Weight  defined.  —  It 
is   proportional   to  quantity  of  matter.  —  Inversely  propor- 
tional to  square  of  the  distance  from  the  earth. — Not  limited 
to  bodies  on  the  earth.  — Not  the  same  as  mass.  —  Cohesion 
defined.  —  Its  power.  —  At   insensible   distances.  —  Weld- 
ing. —  Adhesion    defined.  —  Experiment.  —  Of    solids    to 
solids.  — Of  liquids  to  solids.  —  Capillarity.  —  Familiar  ex- 
amples. — .The  law.  —  Chemism  defined. 

7.  The  fundamental  idea  suggested  by  the  term  Molecule. 

—  By  the  term  Inertia.  —  By  the  term  Attraction.  —  By  the 
term  Repulsion. 

III.— PROBLEMS. 

1 .  With  how  many  times  greater  force  will  a  body  be  at- 
tracted by  a  mass  of  iron  weighing  9  tons,  than  by  a  block 
of  stone  weighing  3  tons,  when  both  are  at  the  same  distance 
from  it?  Ans.  3. 

2.  Two  lead  balls,  one  weighing  5  ounces  and  the  other  12 
ounces,  are  hanging  at  a  distance  of  10  feet  from  a  third ; 
what  relative  degrees  of  force  do  they  exert  upon  it  ? 

3.  One  ball  of  lead  attracts  another  through  a  distance  of 
10  feet  with  a  force  of  8  pounds  ;  what  force  would  it  exert 
if  placed  at  a  distance  of  20  feet?  Ans.  2  pounds. 

4.  A  body  is  at  one  time  50  feet,  and  at  another  75  feet, 


NATURAL   PHILOSOPHY.  19 

from  a  mass  of  rock ;  what  are  the  relative  forces  exerted 
upon  it  in  the  two  positions?  Ans.  9  :  4. 

5.  Two  bodies,  one  weighing  6  pounds,  and  the  other  9 
pounds,  are  attracting  a  third.     The  first  is  at  a  distance  of 
25  feet,  the  second  of  50  feet ;  what  relative  attractions  do 
they  exert  ? 

6         9 
«72  :  if/)25  which,  reduced,  is  the  Ans.  8:3. 

6.  At  the  surface  of  the  earth  a  body  weighs  10  pounds  ; 
what  would  it  weigh  if  carried  to  a  height  of  5  miles  above 
the  surface?  Ans.  9.975  pounds. 

(4005  miles)2  :   (4000  miles)2  : :   10  pounds  :  x. 
x  =  9.975  pounds. 


20  NATURAL   PHILOSOPHY. 


CHAPTER  II. 
THE   THREE  PHYSICAL  FORMS   OF  MATTER. 


SECTION   I. 
APPLICATION  OF  THE  FUNDAMENTAL  IDEAS. 

8.  ATTRACTION  and  REPULSION  acting  upon  the  molecules 
of  bodies  produce  the  three  physical  forms  of  matter,  — 
Solid,  Liquid,  and  Gaseous. 

The  Action  of  the  Molecular  Forces.  —  Between  the 
molecules  of  every  body,  two  sets  of  forces,  attractive  and 
repellent,  are  continually  struggling.  Just  in  proportion  as 
one  or  the  other  prevails,  the  body  will  be  a  solid,  a  liquid,  or 
a  gas.  In  a  solid  body  attraction  prevails,  and  its  molecules 
are  firmly  bound  together.  In  a  liquid  body  the  attraction  is 
almost  equaled  by  the  repulsion,  and  the  molecules  are  left 
free  to  move  easily  among  themselves.  In  a  gaseous  body 
the  repulsion  exceeds  the  attraction,  and  the  molecules  are 
driven  away  from  each  other  to  the  greatest  possible  dis- 
tance. The  solid  rock,  the  mobile  water,  and  the  rushing 
air  are  types  of  these  three  grand  divisions  to  which  all 
bodies  belong. 

Changes  of  Condition  in  Nature.  —  Numerous  and  fa- 
miliar changes  of  form  are  due  to  the  action  of  heat.  Ice, 
for  example,  when  heated,  becomes  water  ;  and  water,  when 
heated  still  more,  rises  in  vapor  to  form  the  floating  clouds. 
In  this  case  molecular  repulsion  is  increased  until  it  is 
stronger  than  molecular  attraction.  Or,  suppose  the  action 
to  be  reversed.  Imparting  their  heat  to  other  bodies,  the 


NATURAL   PHILOSOPHY.  21 

clouds  are  changed  to  water,  and  water  again  to  solid  ice  and 
feathery  snow.  In  this  case  molecular  repulsion  is  dimin- 
ished until  it  is  weaker  than  attraction. 

Artificial  Changes.  —  Imitating  nature,  we  may  to  a 
limited  extent,  by  the  use  of  heat,  change  the  form  of  vari- 
ous bodies  ;  and  numerous  arts  of  life  spring  from  the  appli- 
cation of  this  power.  By  the  repulsive  force  of  heat,  the 
metallic  ores  are  melted,  and  the  useful  metals  obtained.  By 
the  same  force  iron  is  liquefied,  that  it  may  be  molded  into 
requisite  forms  of  strength,  of  beaut}r,  or  of  use,  demanded 
in  the  arts.  The  expansive  force  of  steam  is  but  the  repul- 
sive force  of  heat. 

SECTION  II. 

ON  THE  CHARACTERISTIC  PROPERTIES  OF  SOLIDS. 

9.  The  characteristic  properties  of  solid  bodies  are  Hard- 
ness, Tenacit}^,  Malleability,  Ductility,  and  Crystalline  Form. 
(G.  93-95  ;  A.  59-64.) 

Hardness.  —  The  particles  of  solid  bodies  are  held  to- 
gether by  cohesion,  much  more  firmly  in  some  than  in  others. 
Those  in  which  they  are  held  with  the  greatest  force  will 
most  successfully  resist  the  pressure  of  others.  By  the  term 
HARDNESS,  we  refer  to  that  property  of  solids  which  enables 
them  to  resist  any  action  which  tends  to  wear  or  scratch  their 
particles  away. 

Hardness  does  not  imply  Strength. — A  piece  of  glass 
will  scratch  an  iron  hammer,  which  proves  it  to  be  harder 
than  iron  ;  yet  glass  is  very  fragile,  easily  broken  by  the 
stroke  of  soft  wood,  indeed,  by  almost  any  thing  that  can 
inflict  a  blow. 

Neither  does  Hardness  imply  Density. — The  diamond 
is  the  hardest  of  substances,  while  gold  is  so  soft  as  to  be 
easily  cut  with  a  knife  ;  }*et  gold  is  four  times  as  dense  as  the 
diamond.  Mercury  is  a  fluid,  and,  of  course,  has  no  hard- 
ness ;  yet  it  is  nearly  twice  as  dense  as  the  hardest  steel. 


22  NATURAL  PHILOSOPHY. 

Tempering.  —  The  process  called  tempering,  or  anneal- 
ing, consists  in  regulating  the  hardness  of  a  bod}*  by  the 
action  of  heat.  Steel,  when  in  its  hardest  condition,  is  too 
brittle  to  be  used  in  the  arts  ;  but  by  heating  it  to  a  tempera- 
ture determined  by  the  use  to  be  made  of  it,  and  then  slowly 
cooling  it,  the  steel  may  receive  any  degree  of  hardness 
desirable.  It  may  be  made  almost  as  soft  as  soft  iron,  or  it 
may  become  nearly  as  hard  as  the  diamond. 

Tenacity.  —  When  a  rod  of  iron  is  stretched  in  the  direc- 
tion of  its  length,  it  will  be  found  that  great  force  is  required 
to  pull  it  apart.  The  property,  in  virtue  of  which  a  body 
resists  a  force  which  tends  to  pull  its  parts  asunder,  is  called 
TENACITY. 

Of  Metals.  —  The  metals  are  more  tenacious  than  other 
solids ;  and  among  metals,  iron  in  the  form  of  cast-steel 
stands  at  the  head  of  the  list.  A  rod  of  cast-steel,  the  end 
of  which  has  an  area  of  one  square  inch,  will  support  a 
weight  of  134,256  pounds. 

It  has  been  found  by  experiment  that  the  tenacity  of  a  bar 
is  in  proportion  to  the  area  of  its  cross-section,  and  entirely 
independent  of  its  length. 

It  has  also  been  shown  that  the  tenacity  of  a  metal  is 
greatly  increased  by  drawing  it  into  wire.  The  cables  of 
suspension  bridges  are,  for  this  reason,  made  of  fine  iron  wire 
twisted  together. 

Malleability.  —  The  particles  of  many  solid  bodies  may 
be  displaced  without  overcoming  their  cohesion.  By  the 
blows  of  a  hammer,  the  molecules  of  many  metals  ma}'  be 
shifted  about,  without  breaking  them  apart,  until  the  bodies 
are  reduced  to  the  form  of  thin  plates  or  leaves.  By  passing 
the  metal  between  the  rollers  of  a  rolling-mill,  the  great 
pressure  exerted  will  produce  the  same  effect.  This  prop- 
erty, in  virtue  of  which  a  body  may  be  hammered  or  rolled 
out  into  thin  leaves  or  plates,  is  called  MALLEABILITY. 

Of  Metals.  —  This  property  is  possessed  in  a  high  degree 
by  many  of  the  metals.  Under  the  hammer,  lead  is  the 


HATTTRAL  PHILOSOPHY.  23 

most  malleable  of  the  useful  metals  ;  tin  stands  second,  and 
gold  third,  on  the  list.  In  the  rolling-mill,  gold  is  the  most 
malleable,  silver  is  second,  copper  third,  while  tin  stands  in 
the  fourth  place  on  the  list.  (Silliman's  Physics,  p.  138.) 

Ductility.  —  If,  instead  of  being  reduced  to  thin  plates, 
the  substance  may  be  drawn  into  wire,  the  property  thus 
shown  is  called  DUCTILITY.  This  property  is  closely  allied  to 
malleability,  but  metals  do  not  possess  both  in  an  equal 
degree.  Platinum,  for  example,  which  is  seventh  on  the  list 
of  malleable  metals ,  stands  first  on  the  list  of  those  which 
are  ductile.  This  metal  has  been  drawn  into  wire  finer  than 
a  spider's  thread. 

Crystalline  Form.  —  The  attraction  among  the  molecules 
has  not  brought  them  together  at  random,  nor  in  disorder. 
A  flake  of  snow,  when  seen  through  a  microscope,  is  found 
to  be  as  symmetrically  formed  as  a  swan's  feather;  and 
water  frozen  on  the  window-panes  in  winter  shows  a  beauti- 
ful variety  of  tree-like  forms.  These  definite  and  regular 
forms  in  which  solid  substances  occur  are  called  CRYSTALS  ; 
and  any  process  by  which  they  may  be  obtained  is  called  a 
process  of  CRYSTALLIZATION. 

In  Nature.  —  In  the  formation  of  solid  bodies  their  tend- 
ency to  take  a  crystalline  form  is  almost  universal.  The 
same  substance  generally  takes  the  same  form,  but  in  differ- 
ent substances  the  shapes  of  crystals  may  be  wonderfully 
unlike.  Lead,  in  its  most  common  ore,  called  galena,  is 
found  crystallized  in  cubes.  Specimens  of  these  cubes  are 
often  found  as  perfect  as  could  be  chiseled  by  an  artist. 

But  the  larger  number  of  solid  bodies  around  us  do  not 
appear  to  have  these  definite  crystalline  forms.  They  have 
been  made  solid  under  circumstances  which  did  not  allow 
the  molecular  forces  to  act  freety.  In  many  cases,  however, 
if  we  break  open  a  body  whose  external  form  is  not  regular, 
we  may  discover  that  it  is,  after  all,  a  crystallized  body,  by 
noticing  that  it  is  made  up  of  multitudes  of  small  crystals, 
very  closely  packed  together.  This  is  true  of  many  rocks, 


24  NATURAL  PHILOSOPHY. 

Made  artificially.  —  Even  when  no  indication  of  a  crys- 
talline structure  can  be  seen,  the  substance  can  often  be 
made  to  assume  it  by  some  artificial  process.  The  best 
method  is  to  dissolve  the  solid  in  water  or  some  other  liquid, 
and  allow  the  solution  to  stand  in  a  quiet  place  where  it  may 
evaporate  slowly.  Common  salt  and  alum  are  substances 
which  readily  and  beautifully  illustrate  this  process.  The 
more  slowly  the  water  evaporates,  the  more  perfect  will  the 
crystals  be. 

SECTION   III. 

ON  THE  CHARACTERISTIC   PROPERTIES   OF  LIQUIDS. 

10.  Liquids  have  elasticity  and  some  other  properties  in 
common  with  solid  bodies.  But,  since  the  attraction  and 
repulsion  among  their  molecules  are  very  nearly  equal,  we 
find  that  Mobility  is  their  characteristic  property.  (G.  97, 
98  ;  A.  74.) 

Elasticity.  —  When  submitted  to  pressure,  liquids  are  com- 
pressed ;  and  when  the  pressure  is  removed  they  instantly 
spring  back  to  their  original  volume  :  the}'  are  elastic. 

The  force  with  which  a  liquid  springs  back  to  its  former 

size,  after  being  compressed,  is 
exactly  equal  to  the  force  which 
compressed  it :  it  is,  for  this 
reason,  said  to  be  perfectly 
elastic. 

Compressibility.  —  It     re- 

_  quires  a  very  great  force,  how- 

— «-  ever,  to   compress   a  liquid  in 
the  least  degree  ;  so  great,  that, 

until  improved  means  of  experiment  were  contrived,  liquids 
were  thought  to  be  incompressible.  Water  at  a  freezing 
temperature,  when  pressed  by  a  force  of  fifteen  pounds  to 
the  square  inch,  is  condensed  only  .0000503  of  its  volume. 


NATURAL  PHILOSOPHY,  25 

Attraction  and  Repulsion  nearly  equal.  —  That  the 
attractive  and  repulsive  forces  among  the  molecules  of  a 
liquid  are  not  exactly  equal,  ma}*  be  shown  by  a  pretty  ex- 
periment. 

To  one  end  of  a  scale-beam  (Fig.  6)  a  disk  of  brass  is 
suspended,  and  accurately  balanced  by  weights  in  the  oppo- 
site scale-pan.  Then  let  the  disk  be  brought  to  rest  upon 
the  surface  of  water  in  a  vessel,  and  it  will  be  held  there 
with  considerable  force.  If  the  disk  be  two  inches  in  diam- 
eter, weights  equal  to  two  hundred  grains  may  be  placed 
upon  the  opposite  pan  before  it  will  be  torn  from  the  water. 
But  we  notice  that  a  film  of  water  still  adheres  to  the  disk, 
having  been  torn  away  from  the  water  beneath  it.  The 
weight  of  two  hundred  grains  has  simpty  overcome  the  cohe- 
sion of  the  water.  We  thus  learn  that  the  attraction  is  a 
trifle  stronger  than  the  repulsion. 

Mobility.  —  But  the  attractive  and  repulsive  forces  are 
nearly  balanced ;  and,  if  we  now  remember  that  water  con- 
sists of  molecules,  it  is  not  more"  difficult  to  see  that  there 
must  be  freedom  of  motion  among  them,  than  it  is  to  see 
that  shot,  or  smooth  balls  of  any  other  kind,  will  roll  easily 
upon  each  other. 

The  molecules  of  water  are  balls  infinitely  smaller  than 
shot,  but,  while  the  most  powerful  microscope  fails  to  reveal 
them,  the  mind  can  see  them,  so  small,  so  round  and  smooth, 
that  they  roll  and  glide  among  themselves  with  the  greatest 
freedom. 

This  freedom  of  motion  among  the  molecules  of  a  substance 
is  called  MOBILITY. 

Mobility  is  the  property  of  a  liquid  which  makes  it  differ 
from  a  solid.  Destroy  the  mobility  of  water,  and  it  becomes 
a  solid, — ice.  Impart  mobility  to  a  solid,  and  it  ceases  to 
be  a  solid  ;  it  becomes  a  liquid,  as  when  ice  is  melted. 


26  NATURAL  PHILOSOPHY. 

SECTION   IV. 
ON  THE   PRESSURE  OF  LIQUIDS. 

11.  At  any  point  inside  of  a  body  of  liquid  at  rest,  there 
is  equal  pressure  from  all  directions. 

Hence  a  fluid  will  rest  only  when  its  upper  surface  is  level ; 
but  the  level  surface  of  a  large  body  of  water  is  convex.  (G. 
105,  108,  110;  A.  304.) 

Liquids  press  in  all  Directions.  —  In  order  to  see  that, 
because  the  particles  of  a  liquid  are  free  to  move,  they 
must  be  exerting  pressure  in  all  directions, 
we  will  suppose  a  number  of  very  smooth 
balls  to  be  arranged  as  in  Fig.  7.  The 
weight  of  the  ball  A  will  be  a  downward 
pressure  upon  the  balls  B  and  C.  These, 
being  free  to  move,  will  be  pushed  aside. 
The  ball  B,  moving  toward  the  left,  will  push  between  the 
balls  D  and  E,  while  the  ball  E,  moving  upward,  will  exert 
an  upward  pressure.  Just  so  the  small  molecules  of  a  liquid 
are  exerting  pressure  downward,  upward,  and  laterally. 
This  pressure  is  due  to  gravitation. 

Moreover,  the  pressure  of  the  liquid  must  be  exerted 
Equally  in  all  Directions.  —  For,  if  the  pressure  at  any 
point  were  greater  in  one  direction  than  another,  the  liquid 
would  move  in  that  direction  on  account  of  its  mobility.  If, 
then,  the  liquid  is  at  rest,  the  pressures  in  all  directions  must 
be  just  balanced. 

Experimental  Illustration.  —  An  experiment  may  help 
to  illustrate  this  principle.  If  a  disk  of  metal  be  held  in  the 
middle  of  a  jar  of  water,  it  is  easy  to  see  that  it  must  be 
pressed  downward  by  the  weight  of  the  water  just  above  it ; 
but  it  may  not  be  so  clear  that  it  is  pushed  upward  by  an 
equal  force.  Taking  a  lamp-chimney,  and  putting  the  string 


NATURAL  PHILOSOPHY. 


27 


handle  of  the  disk  (Fig.  8)  through  it,  hold  the  disk  tightly 
against  the  lower  end  of  the  tube  until  it  is  pushed  down 
to  the  middle  of  the  water. 
Now  drop  the  string :  the 
heavy  disk  does  not  sink, 
but  remains  tightly  pressed 
upward  against  the  tube  by 
the  water.  If  water  be  al- 
lowed to  enter  the  tube,  it 
will  press  down  upon  the 
disk ;  and,  when  it  has 
filled  the  tube  almost  to  a 
level  with  the  water  out- 
side, then  the  disk  falls, 
suggesting  that  the  upward 


pressures 


Fig.  8. 


and    downward 
are  equal. 
Another   Illustration. 

— Numerous  simple  experi- 
ments might  be  given  to 
illustrate  this  important  principle :  one  other  must  suffice. 
Glass  is  eminently  brittle.  It  ma}'  be  blown  into  sheets  as 
thin  as  the  finest  paper-cambric.  In  this  condition,  the 
weight  of  a  few  grains  resting  upon  it  in  the  air  would  crush 
it.  Yet,  placed  near  the  bottom  of  the  deepest  cistern,  it 

B  will   support  the  weight  of 
all  the  water  above  it,  and  re- 
main unbroken.     This  could 
E  not   happen  if  the  pressure 
of  the  water  upon  it  were  not 
equal  from  all  directions. 
The  Surface  of  Water  at 


Fig.  9. 


Rest  is  level.  —  The   truth 


of  this  principle  may  be  seen  by  attentively  examining  Fig. 
9,  which  represents  a  section  of  a  vessel  containing  water, 
the  surface  of  which  has  for  the  moment  been  thrown  into 


28  NATURAL   PHILOSOPHY. 

the  position  indicated  by  the  line  A  E.  Refer  to  an}T  two 
points  in  the  water,  as  h  and  K.  We  see  that  the  down- 
ward pressure  at  h  would  be  the  weight  of  the  water  above 
that  point,  —  a  column  m  h.  But  the  pressure  at  that  point 
is  equal  in  all  directions,  so  that  the  water  between  h  and  K 
would  be  pressed  toward  K  by  a  force  equal  to  the  weight 
of  the  column  m  h.  In  just  the  same  way  we  may  show 
that  at  K  the  water  is  being  pressed  toward  h  by  a  force 
equal  to  the  weight  of  the  column  n  K.  The  column  m  h 
is  greater  than  n  K  ;  and,  since  the  water  is  free  to  move,  it 
will  yield  to  the  greater  pressure,  and'go  toward  K  until  the 
two  forces  are  equal.  The  two  forces  will  be  equal  only 
when  m  and  n  are  in  the  same  level  surface,  a  b. 

But  a  level  Surface  is  convex The  surface  of  water 

will  be  at  rest  when  the  force  of  gravitation  acts  upon  all 
points  of  it  alike.  That  the  attraction  of  the  earth  may 
be  equal  on  all  points,  they  must  be  equally  distant  from 
the  center  of  the  earth  :  to  be  at  the  same  distance  from  the 
center  of  the  earth,  they  must  form  a  curved  surface.  In 
case  of  large  bodies  of  water,  of  the  oceans  for  example, 
the  convexity  can  be  seen.  It  is  shown  by  the  ancient 
observation  that  the  topmast  of  an  approaching  ship  is  the 
part  first  seen  from  port. 

12.  Since  the  surface  of  water  at  rest  must  be  level,  we 
infer  that  water  confined  in  pipes  or  close  channels  will  always 
rise  in  them  as  high  as  the  source  from  which  it  comes. 

Upon  this  principle  cities  are  often  supplied  with  water. 

The  same  principle  explains  the  phenomena  of  springs 
and  artesian  wells. 

Water  in  Pipes  will  rise  as  high  as  its  Source.  —  No 

matter  what  ma}'  be  the  shape  of  the  vessel,  the  surface  of 
the  liquid  it  holds  must  be  just  as  high  in  one  part  of  it  as 
in  another.  Moreover,  a  pipe  leading  from  a  vessel  is  a  part 
of  the  vessel  which  holds  the  water. 


NATUBAL  PHILOSOPHY. 


29 


The  vessel  shown  in  Fig.  10  has  a  very  irregular  shape. 
There  is  first  the  large  vase  at  the  left  hand,  then  the 
horizontal  tube,  and  finally  the  tubes  reaching  upward  from 
the  last ;  yet  it  is  all  one  vessel,  because  the  water  can  pass 
freely  from  one  part  to  another. 

If  water  is  poured  into  the  vase,  it  will  rise  just  as  fast  in 
the  tubes,  and  will  at  last  stand  at  the  same  height  in  all 
parts,  as  the  picture  shows  it  to  be. 

The  Supply  of  Water  to  Cities.  —  A  pipe  leading  from 
a  reservoir  of  water  on  a  hill  outside  a  city  may  be  buried 


Fig.  10. 

in  the  ground,  passed  down  the  hillside  and  through  the 
streets,  and  be  provided  with  branches  leading  into  cisterns 
in  every  dwelling.  Unless  these  cisterns  are  higher  than  the 
water  in  the  distant  reservoir,  the  water  will  flow  down 
the  hillside,  through  the  streets,  and  up  the  branches,  into  the 
dwellings,  and  supply  them  all  with  water.  Many  cities 
are  in  this  way  convenient!}'  supplied  with  abundance  of 
water,  not  only  for  private  dwellings,  but  also  for  public  foun- 
tains and  manufacturing  purposes. 

Springs.  —  The   rocks  which   compose  the  earth  are  ar- 


30 


NATURAL   PHILOSOPHY. 


ranged  in  layers,  called  strata,  which  are  generally  more  or 
less  oblique  as  represented  in  Fig.  1  1  .  Some  of  these  strata 
will  allow  water  to  soak  through  them  :  others  will  not.  In 
the  figure  the  dotted  portions  a  a  a  indicate  the  porous 
strata. 

Now,  water  falling  on  the  surface  of  the  earth  at  c  will 
settle  through  the  loose  or  porous  material  until  it  reaches 
the  rock,  which  it  can  not  penetrate.  Flowing  along  the 
surface  of  this  rock,  it  will  issue  from  the  hillside  at  S,  and 
thus  form  a  spring. 

Artesian  Wells.  —  Again,   the   water,   falling   upon   the 


Fig.  11. 

surface,  and  passing  through  other  porous  layers,  at  length 
comes  in  contact  with  a  rock  which  it  can  not  penetrate,  and 
flows  along  its  surface.  The  basin-shaped  part,  a  a,  of  the 
porous  layer,  would  thus  in  time  become  filled  with  water ; 
indeed,  the  entire  layer  reaching  to  the  surface  of  the  earth 
in  both  directions  might  thus  be  filled.  If,  then,  a  well  as 
W  be  sunk  through  the  mass  down  to  this  saturated  layer, 
the  water  will  collect  in  the  well,  and  rise  sometimes  to  the 
surface  of  the  ground  above,  and  sometimes  it  even  spouts  in 
jets  many  feet  above  the  surface. 

Such  wells  are  often  bored  to  very  great  depths,  and  are 


NATURAL   PHILOSOPHY. 


31 


called  artesian  wells.  One  of  these  wells  was  bored  in 
Louisville,  Ky.,  to  the  depth  of  2,086  feet.  Another  in  St. 
Louis  has  a  depth  of  2,199  feet.  The  supply  of  water  fur- 
nished is  often  very  abundant.  The  famous  Grenelle  well,  in 
Paris,  yields  daily  600,000  gallons. 


13.  The  pressure  of  a  liquid  on  the  bottom  of  the  vessel 
which  holds  it  is  independent  of  the  shape  of  the  vessel. 

It  depends  on  the  depth  of  the  liquid,  and  the  area  of  the 
bottom  of  the  vessel. 

It  equals  the  weight  of  a  column  whose  base  is  the  base 
of  the  vessel,  and  whose  height  is  the  depth  of  the  liquid. 
(G.  104;  A.  303.) 

The  Pressure  is  independent  of  the  Shape  of  the 
Vessel.  —  This  may  be  proved  by  experiment.  The  essen- 
tial parts  of  an  apparatus  for  this  purpose  are  represented  in 
Fig.  12.  A  glass  tube, 
A  B,  bent  twice  at  right 
angles,  contains  mercu- 
ry. The  height  of  mer- 
cury in  one  arm  is  shown 
by  a  graduated  scale, 
and  to  the  other  arm 
vessels  of  various  forms 
and  heights  may  be  at- 
tached. When  a  vessel, 
G,  is  filled  with  water, 
the  fluid  presses  upon  the  mercury  at  A,  and  pushes  it  up 
in  the  arm  C  D  ;  the  height  to  which  it  rises  being  shown 
by  the  graduated  scale.  Now  let  the  vessel  be  removed,  and 
another,  in  the  form  shown  at  E,  be  put  in  its  place.  If 
water  be  poured  into  this  vessel  until  it  stands  as  high  as 
it  did  in  the  other,  the  mercury  will  be  seen  to  rise  in  C  D  to 
the  same  point  as  before.  Vessels  of  various  other  forms 
may  be  used ;  but,  if  all  are  of  the  same  height,  the  water 


Fig.  12. 


32  NATURAL  PHILOSOPHY. 

which  fills  them  will  push  the  mercury  to  the  same  point  on 
the  scale.  We  infer  that  the  pressure  of  a  fluid  downward 
is  quite  independent  of  the  shape  of  the  vessel  and  of  the 
quantity  of  fluid  it  contains. 

The  Pressure  depends  on  the  Depth  of  the  Liquid 

If  a  tube  twice  as  high  as  the  vessel  E,  in  Fig.  12,  be  used, 
and  filled  with  water,  the  mercury  will  be  seen  to  rise  just 
twice  as  far  as  when  the  other  vessels  were  employed  ;  and  by 
repeated  experiment  it  is  found  that  the  pressure  is  in  pro- 
portion to  the  height  of  the  column  of  water  which  exerts  it. 
The  Pressure  depends  also  on  the  Area  of  Base.  —  In 
these  experiments  the  area  receiving  the  pressure  at  the  bot- 
tom of  the  vessels  is  the  same  for  all.  If  next  we  suppose 
the  bottom  of  the  vessel  to  be  made  just  twice  as  large,  there 
would  be  just  twice  as  much  water  resting  upon  it,  and 
therefore  just  twice  the  downward  pressure.  In  any  case,  the 
pressure  is  in  proportion  to  the  area  of  the  base  of  the  vessel. 
To  calculate  the  Pressure.  —  If  the  pressure  depends 
only  on  the  size  of  the  base  and  the  height  of  the  column, 
then  it  must  equal  the  weight  of  a  column  whose  base  is 
the  base  of  the  vessel,  and  whose  height  is  the  depth  of  the 
liquid.  Now,  one  cubic  foot  of  water  weighs  62J  pounds ; 
and,  if  the  number  of  cubic  feet  of  water  which  exerts  the 
pressure  be  multiplied  by  62^,  the  amount  of  pressure  in 
pounds  will  be  obtained. 

Illustration.  —  Thus,  suppose  a  vessel,  represented  by 
E  F  C  D  in  Fig.  13,  to  be  full  of 
water  :  the  pressure  on  its  bottom 
is  the  weight  of  the  column  A  B 
C  D.  Let  the  area  of  the  bottom 
be  three  square  feet,  and  the  depth 
of  the  water  be  eight  feet ;  then 
the  pressure  is  the  weight  of  24 
cubic  feet  of  water,  and  24  X  62J 
pounds,  or  1,500  pounds,  is  the  pressure  exerted. 

Since   the   pressure   is   equal   in   all   directions,   we   may 


NATURAL   PHILOSOPHY.  33 

obtain  the  amount  of  pressure  against  any  portion  of  sur- 
face, either  in  the  bottom  or  sides  of  the  vessel,  by  finding 
the  weight  of  a  column  of  water  whose  base  is  the  surface 
pressed  upon,  and  whose  height  is  the  depth  of  the  water  to 
the  middle  point  of  that  surface. 

For  example  :  suppose  we  would  know  how  much  pressure 
is  borne  by  one  square  foot  of  the  side  of  a  vessel  at  a  depth 
of  ten  feet  below  the  surface  of  the  water.  We  must  under- 
stand that  ten  feet  is  the  distance  from  the  top  of  the  water 
to  the  middle  point  of  the  square  foot ;  then  the  pressure  will 
be  the  weight  of  a  column  of  water  whose  base  is  one  square 
foot  and  whose  height  is  ten  feet.  Such  a  column  will  con- 
tain ten  cubic  feet  of  water,  and  its  weight  will  be  10  x  62^ 
pounds. 

14.  A  solid  body,  when  immersed  in  a  fluid,  is  pushed 
upward  by  it  with  a  force  equal  to  the  weight  of  the  fluid  it 
displaces. 

It  follows  from  this  principle  :  — 

1st,  That  a  solid  body,  lighter  than  water,  will  sink  far 
enough  to  displace  a  quantit}*  of  water  just  equal  to  its  own 
weight. 

2d,  That  a  solid  body,  heavier  than  water,  will  weigh  less 
in  water  than  in  air,  the  difference  being  the  weight  of  the 
water  displaced  by  it.  (G.  116,  119  ;  A.  320,  325-327.) 

Solid  Bodies  in  Water  are  pressed  upward.  —  If,  for 

example,  a  piece  of  wood  be  pushed  dowi>  into  a  vessel  of 
water,  we  find  it  struggling  to  rise  to  the  surface :  it  is 
pressed  upward  by  the  water  under  it,  and  considerable  force 
of  the  hand  is  required  to  keep  it  down.  Or,  if  a  stone  be 
suspended  in  water,  it  is  lighter  than  when  in  air :  the 
water  under  it  pushes  upward  against  it,  and  thus  supports  a 
part  of  its  weight. 

With  Force  equal  to  the  Weight  of  Water  displaced. 
—  Let  us  suppose  that  a  block  of  marble  is  suspended  in  a 


34 


NATURAL  PHILOSOPHY. 


Fig.  14. 


vessel  of  water  (Fig.  14).  The  upward  pressure  against  its 
lower  surface,  a  6,  is  equal  to  the  downward  pressure  of  the 
water  at  that  depth  ;  and  this  downward  pressure  is  equal  to 
the  weight  of  the  column  of  water,  efba. 
Now,  a  part  of  this  upward  pressure  sus- 
tains the  column  of  water,  efcd,  and  the 
rest  of  it  is  exerted  upon  the  marble.  To 
sustain  the  column,  efcd  requires  an 
upward  pressure  equal  to  its  weight ;  and 
hence  there  is  left  a  pressure  against  the 
surface  a  6,  equal  to  the  weight  of  a  column 
of  water,  a  b  c  d,  but  this  water  is  dis- 
placed by  the  marble.  The  upward  pressure 
against  the  block  is  therefore  equal  to  the 
weight  of  the  fluid  displaced. 
The  Principle  of  Archimedes.  —  We  owe  the  discovery 
of  this  important  principle  to  Archimedes,  one  of  the  most 
eminent  philosophers  of  antiquity ;  and  to  this  day  it  is 
called  the  PRINCIPLE  OF  ARCHIMEDES.  Its  applications  are 
numerous.  It  helps  the  chemist  to  distinguish  one  substance 
from  another,  and  the  merchant,  often,  to  judge  of  the 
purity  and  value  of  his  merchandise.  In  any  case  it  ena- 
bles the  inquirer  to  determine  the  size  or  volume  of  a  solid 
body,  however  irregular  ;  and  it  has,  moreover,  led  to  valua- 
ble improvements  in  marine  architecture  and  in  other  arts. 

If  the  Solid  is  lighter  than  Water.  —  The  weight  of 
the  water  displaced  by  a  block  of  wood  will  just  equal  the 
weight  of  the  wood  itself.  A  pound  of  wood  will  displace 
a  pound  of  water.  But  a  pound  of  wood  is  larger  than  a 
pound  of  water,  so  that  only  part  of  the  wood  will  be  im- 
mersed. A  tin  basin  and  a  wooden  bowl  of  the  same  size 
will  displace  an  equal  volume  of  water,  if  the  walls  of  the 
basin  are  thin  enough  so  that  the  two  bodies  have  the  same 
weight.  Upon  this  principle  iron  ships  are  built.  An  iron 
ship  will  sink  no  farther  than  one  of  wood  of  the  same  size, 
provided  the  walls  of  iron  are  so  thin  that  the  two  ships 
shall  be  of  the  same  weight. 


KATUKAL  PHILOSOPHY.  35 

If  the  Solid  is  heavier  than  Water,  —  If  a  solid  is 
heavier  than  water,  the  upward  pressure  of  the  fluid  can 
support  only  a  part  of  its  weight.  The  weight  supported 
will  be  equal  to  the  weight  of  the  water  which  the  solid 
displaces.  Thus,  for  example,  a  piece  of  marble  which 
weighs  10  ounces  in  air  will  be  found  to  weigh  only  6.3 
ounces  in  water.  The  upward  pressure  of  the  water  is 
equal  to  the  difference,  3.7  ounces;  and  this  is  the  weight 
of  the  water  which  the  marble  displaces,  and  whose  bulk 
is,  of  course,  just  equal  to  the  bulk  of  the  marble. 

15.  The  specific  gravity  of  a  substance  is  its  weight  com- 
pared to  the  weight  of  an  equal  volume  of  some  other  body 
taken  as  a  standard. 

To  obtain  it,  different  methods  must  be  taken,  according 
as  the  body  is  a  gas,  a  liquid,  or  a  solid.  (G.  123,  125, 
130.) 

Specific  Gravity.  —  The  specific  gravity  of  a  substance 
shows  how  many  times  heavier  it  is  than  an  equal  volume 
of  some  other  body.  The  standards  used  are  water  and 
air;  water  for  all  solid  and  liquid  bodies,  and  air  for  all 
gases.  In  chemistry  hydrogen  instead  of  air  is  the  standard 
for  gases.  Then,  when  we  say,  for  instance,  that  the  spe- 
cific gravity  of  gold  is  19,  we  only  mean  that  a  cubic  inch 
of  gold  will  weigh  19  times  as  much  as  a  cubic  inch  of 
water.  The  specific  gravity  of  oxygen  gas  is  1.106:  that 
is  to  say,  a  cubic  inch  of  oxygen  gas  will  weigh  1.106  as 
much  as  a  cubic  inch  of  air.  Or,  compared  with  Irydrogen, 
its  specific  gravity  is  16  :  that  is  to  say,  a  cubic  inch  of  oxy- 
gen weighs  16  times  as  much  as  a  cubic  inch  of  Irydrogen. 
The  following  simple  rule  must  evidently  cover  all  cases  of 
finding  specific  gravity :  Divide  the  weight  of  the  body  by 
the  weight  of  an  equal  volume  of  the  standard. 

How  shall  these  two  Weights  be  found?  —  The  weight 
of  the  body  whose  specific  gravity  is  sought  can  be  found 


36 


NATURAL   PHILOSOPHY. 


directly  with  the  balance,  but  the  weight  of  an  equal  volume 
of  the  standard  can  not.  It  is  not  easy  to  know  the  exact 
volume  of  the  body,  which  is  often  very  irregular  in  shape. 
Different  methods  of  experiment  must  be  used  in  different 
cases. 

I.  — OF  GASES. 

How  may  the  Specific  Gravity  of  a  Gas  be  found  ?  — 

To  obtain  the  specific  gravity  of  a  gas,  divide  the  weight  of  a 
convenient  portion  of  it  by  the  weight  of  an  equal  portion  of 
air  or  hydrogen. 

To  get  the  weight  of  equal  portions  of  gases,  is,  however, 
a  difficult  process,  requiring  many  precautions.  Without 
trying  ^o  give  the  details  of  the  operation,  we  may  describe 
it  in  general  terms.  A  glass  globe  is  first  weighed  when 

full  of  air  (Fig.  15).  The 
air  is  then  taken  out  of  it  by 
means  of  an  air-pump,  and 
the  globe  is  again  weighed. 
The  difference  in  these 
weights  is  the  weight  of  the 
globe-full  of  air.  The  globe 
is  then  filled  with  the  gas 
whose  specific  gravit}T  is  de- 
sired, and  again  weighed. 
The  difference  between  this 
weight  and  that  of  the  empty 
globe  is  the  weight  of  the 
globe-full  of  gas.  The  spe- 
cific gravity  is  obtained  from  these  weights  of  equal  volumes 
of  gas  and  air. 

II.  —  OF   LIQUIDS. 

How  may  the  Specific  Gravity  of  a  Liquid  be  found  ? 

—  To  obtain  the  specific  gravity  of  a  liquid,  divide  the  weight 
of  a  convenient  volume  of  it  by  the  weight  of  an  equal  vol- 
ume of  water. 


Pig.  15. 


NATURAL   PHILOSOPHY. 


37 


The  experiments  by  which  to  find  the  weights  of  equal  vol- 
umes of  the  two  liquids  may  be  made,  — 

1st,  With  a  balance. 

2d,  With  a  hydrometer. 

3d,  With  a  solid  bulb. 

With  a  Balance.  —  The  most  direct  method  of  getting  the 
specific  gravity  of  a  liquid  is  to  weigh  equal  quantities  of  it 
and  water,  and  then  divide  the  weight  of  the  liquid  by  that 
of  the  water.  To  facilitate  the  operation,  "  specific  gravity 
bottles"  are  made,  which  hold  just  one  thousand  grains  of 
pure  water.  The  weight  of  the  bottle  being  known,  a  single 
operation  with  the  balance  will  give  the  weight  of  the  liquid, 
and  then  its  specific  gravity  may  be  speedily  calculated. 

With  a  Hydrometer.  —  A  common  form  of  this  instru- 
ment is  represented  in  Fig.  16.  It  consists  of 
a  glass  tube,  with  two  bulbs  near  its  lower 
end.  The  tube  and  upper  bulb  are  full  of  air, 
which  renders  the  instrument  lighter  than 
water.  The  lower  and  smaller  bulb  contains 
shot  enough  to  keep  the  instrument  in  an  erect 
position,  when  placed  in  a  liquid,  as  shown 
in  the  figure.  A  graduated  scale  is  fixed  to 
the  stem,  to  indicate  the  depth  to  which  the 
instrument  sinks  in  different  liquids. 

Explain  the  Action  of  this  Instrument. 
—  The  action  of  the  Irydrometer  can  be  read- 
ily explained  by  means  of  a  piece  of  wood, 
several  inches  long  and  an  inch  square,  hav- 
ing its  lower  end  loaded  with  wire.  If  this  be  put  into  a 
vessel  of  water,  it  will  sink  to  a  certain  depth,  and  remain 
upright.  If  it  sinks  ten  inches,  then  ten  cubic  inches  of 
water  are  displaced  by  it.  If  the  instrument  be  put  into 
a  vessel  of  alcohol,  it  will  sink  deeper :  suppose  it  be 
twelve  inches ;  thf^.  twelve  cubic  inches  of  alcohol  are  dis- 
placed. But,  according  to  the  principle  of  Archimedes,  the 
fluid  displaced  is  equal  in  weight  to  the  body  floating  in  it, 


38  NATURAL  PHILOSOPHY. 

Hence  ten  cubic  inches  of  water  have  the  same  weight  as 
twelve  cubic  inches  of  alcohol ;  or  alcohol  is  |f  as  heavy  as 
water.  Its  specific  gravit}-  is,  therefore,  ^f  =  .833  +  . 

Making  the  instrument  of  glass,  and  giving  it  the  form 
seen  in  Fig.  16,  renders  it  more  convenient  and  more  ac- 
curate, but  does  not  alter  the  principle  on  which  it  acts. 

The  Graduation. — The  graduation  of  the  scale  is  arbi- 
trary, and  varies  in  different  forms  of  the  instrument.  The 
zero  usually  marks  the  point  to  which  the  hydrometer  sinks 
in  pure  water,  and  the  degrees  above  and  below  show  how 
far  the  instrument  may  sink  in  liquids  respectively  lighter 
and  heavier  than  water. 

By  the  Use  of  a  Bulb.  —  According  to  the  principle  of 
Archimedes,  a  heavy  bulb  of  glass,  or  other  convenient  sub- 
stance, when  weighed  in  an}'  liquid,  will  lose  a  part  of  its 
weight  just  equal  to  the  weight  of  an  equal  bulk  of  that 
liquid.  Hence,  weigh  a  bulb  of  glass  in  air,  afterward  in 
water,  and  then  in  the  liquid  whose  specific  gravity  is  desired. 
The  losses  of  weight  it  sustains  will  be  the  weights  of  equal 
bulks  of  the  two  liquids,  and  from  these  weights  the  specific 
gravit}T  ma}'  be  obtained. 

To  illustrate  this  method,  suppose  the  specific  gravity  of 
alcohol  is  to  be  found.  A  bulb  of  glass,  weighed  in  air  and 
then  in  water,  is  found  to  lose  325  grains.  Its  loss  in  alcohol 
is  found  to  be  257  grains.  Then  J|-Jr=  .79+  is  the  specific 
gravity  of  the  alcohol.  Alcohol,  with  this  specific  gravity 
contains  no  water :  a  higher  specific  gravity  shows  the  pres- 
ence of  water. 

III.  — OF  SOLIDS. 

How  may  the  Specific  Gravity  of  a  Solid  be  found  ? 

—  To  find  the  specific  gravity  of  a  solid  body,  divide  the 
weight  of  a  convenient  portion  of  it  by  the  weight  of  an 
equal  volume  of  water. 

There  are  two  important  cases  of  common  occurrence  :  — 

1st,  The  solid  is  heavier  than  water. 

2d,  The  solid  is  lighter  than  water. 


KATURAL  PHILOSOPHY. 


39 


Of  a  Solid  heavier  than  Water.  —  Divide  the  weight  of 
the  body  in  air,  by  its  loss  of  weight  in  water.  The  princi- 
ple of  Archimedes  explains  this  rule. 

Thus  the  weight  of  a  piece  of  marble  in  air  is  ten  ounces, 
and  in  water  it  is  6.3  ounces:  the  difference,  3.7  ounces,  is 
the  weight  of  a  bulk  of  water  equal  to  the  size  of  the  marble. 
Then,  |?  =  2.7  is  the  specific  gravity  of  this  solid. 

Describe  the  Experiment.  —  The  experiment  is  con- 
ducted in  the  following  manner  :  Let  the  specific  gravity  of 
iron  be  desired.  A  fragment 
of  iron  of  convenient  size  is 
hung  from  the  bottom  of  one 
scale-pan  of  a  balance,  and 
weighed.  It  is  then  immersed 
in  a  vessel  of  water  (see  Fig. 
17),  and  its  weight  again  de- 
termined. 

Of  a  Solid  lighter  than 
Water If  the  solid  be  light- 
er than  water,  the  operation 
is  more  complex.  If  the  light 
body  be  compelled  to  sink  in 
water  by  fastening  to  it  some  heavier  bod}r,  their  loss  of 
weight  will  represent  the  upward  pressure  of  the  water  upon 
them  both.  If  the  heavy  body  alone  be  weighed  in  water, 
its  loss  will  represent  the  upward  pressure  against  it  alone. 
If  the  upward  pressure  against  the  heavy  body  be  subtracted 
from  the  upward  pressure  against  both,  the  difference  must 
represent  the  upward  pressure  against  the  light  body  alone, 
and  hence  the  weight  of  a  quantity  of  water  equal  to  its 
bulk. 

Illustration. — A  body  weighed  200  grains  in  air.  When 
attached  to  a  piece  of  lead,  both  weighed  1,936  grains  in  air, 
and  1,460  grains  in  water;  suffering  a  loss  of  476  grains. 
The  lead  itself,  when  weighed  in  water,  lost  152  grains.  The 
upward  pressure  against  the  light  body  alone  must  have  been 


Fig.  17. 


40 


NATURAL   PHILOSOPHY. 


476  —  152  =  324  grains.  Then,  200  grains,  the  weight  of 
the  light  bod}'  in  air,  divided  by  324  grains,  the  weight  of  an 
equal  bulk  of  water,  is  the  specific  gravity  desired. 

In  the  following  table  the  specific  gravities  of  several  im- 
portant substances  are  arranged  for  reference. 


I.  — Of  Gases,  at  32°  F.     Barometer,  30  inches. 


NAMES. 

SPECIFIC 
GRAVITY. 

NAMES. 

SPECIFIC 
GRAVITY. 

Air     .              ... 

1.000 

Nitrogen 

0  972 

OxVfifen 

1  106 

Carbonic  acid 

1  529 

Hydrogen   

0.0692 

Olefiant  gas 

0  978 

II.  —  Of  Liquids,  at  39°  F. 


NAMES. 

SPECIFIC 
GRAVITY. 

NAMES. 

SPECIFIC 
GRAVITY. 

Water  (distilled) 

1  000 

Ether  

0  723 

Sea-water   
Milk  

1.026 
1.030 

Naphtha.     .     .         . 
Oil  turpentine 

0.847 
0.870 

Alcohol  (absolute)   .     . 
Olive-oil      

0.792 
0.915 

Wine  of  Burgundy  . 
Mercury  (32°  F.)  .     . 

0.991 
13.598 

III.  — Of  Solids,  at  39°  F. 


NAMES. 

SPECIFIC 
GRAVITY. 

NAMES. 

SPECIFIC- 
GRAVITY. 

Platinum  (rolled)     .     . 
Gold  (stamped)    .     .     . 

22.069 
19.362 

7  2 

Silver  (cast)  .  .  . 
Diamond  .... 
Marble 

10.47 
3.50 

2  837 

Steel 

7  8 

1.92 

Lead  (cast)      .... 
Copper  " 

11.3 

8  78 

Flint-glass  .... 
Ice  .  . 

3.329 
0.93 

Brass 

8  38 

Pine  wood  .... 

0.66 

NATURAL   PHILOSOPHY. 


41 


16.  If  an  external  pressure  be  exerted  anywhere  upon  a 
liquid,  the  same  amount  of  pressure  will  be  transmitted  in 
eveiy  direction. 

It  will  act  with  the  same  force  on  equal  surfaces,  and  in 
directions  at  right  angles  to  them.  This  principle  is  known 
as  PASCAL'S  LAW.  (G.  99,  109  ;  A.  298,  299.) 


The  equal  Transmission  of  Pressure.  —  To 

the  principle  stated  above,  let  a  vessel, 
represented  in  section  by  Fig.  18,  be 
quite  filled  with  water.  In  the  sides  of 
the  vessel  are  several  apertures,  A,  B, 
C,  D,  and  E,  closed  with  movable  pis- 
tons. Let  the  area  of  each  piston  be 
one  square  inch,  and  suppose  a  weight 
of  two  pounds  be  placed  upon  the  pis- 
ton A.  It  will  be  found  that  the  pressure 
on  each  piston  will  be  increased  by  a 


illustrate 


Fig.  18. 


force  of  just  two  pounds.  Thus  E  will  be  pushed  upward 
by  a  force  of  two  pounds,  while  B  and  D  will  at  the  same 
time  be  pushed  in  opposite  directions,  each  with  a  force  of 
just  two  pounds.  No  matter  how 
numerous  these  pistons  may  be,  nor 
in  what  direction  they  may  be  in- 
serted, each  will  be  found  exerting 
a  two-pound  pressure  greater  than 
before  under  the  influence  of  a  force 
of  two  pounds  acting  at  A.  Every 
square  inch  in  the  entire  surface  of 
the  vessel  will  receive  a  pressure  of 
two  pounds. 

Experiment.  —  Then,  suppose 
two  C3Tlinders,  one  just  twice  as  large 
as  the  other,  to  be  joined  together  by  a  tube  at  their  bottoms 
(Fig.  19),  and  let  there  be  a  piston  fitting  each  cylinder 
exactly,  and  carrying  a  table  as  shown  in  the  picture.  Now, 


Fig.  19. 


42 


NATURAL  PHILOSOPHY. 


according  to  the  principle  just  learned,  if  a  one-pound  weight 
be  put  upon  the  small  table,  it  will  balance  a  two-pound 
weight  upon  the  other. 

If  one  cylinder  be  one  hundred  times  larger  than  the  other, 
then  one  pound  on  the  small  table  will  balance  one  hun- 
dred pounds  on  the  large  one. 

The  experiment  shows  that  if  an  external  pressure  be  made 
on  any  part  of  the  surface  of  a  fluid,  the  pressure  received 
by  any  other  part  of  the  surface  will  be  in  proportion  to  its 
area. 


Fig.  20. 

Application  of  this  Principle. — The  hydrostatic  press 
acts  upon  the  principle  just  explained.  It  is  a  machine  by 
which  a  small  force  may  be  made  to  exert  a  great  pressure. 
Its  construction  may  be  understood  by  examining  Fig.  20. 

Two  metallic  cylinders,  A  and  B,  of  different  sizes,  are 


NATURAL  PHILOSOPHY.  43 

joined  together  by  a  tube  K.  In  the  small  cylinder  there  is 
a  piston,  p,  which  can  be  moved  up  and  down  by  the  handle 
M.  In  the  large  cylinder  there  is  also  a  piston,  P,  having  at 
its  upper  end  a  large  iron  plate  which  moves  freely  up  and 
down  in  a  strong  framework,  Q.  Between  the  iron  plate 
and  the  top  of  this  framework,  the  body  to  be  pressed  is 
placed. 

When  the  small  piston  is  raised,  the  cylinder  A  is  filled 
with  water  drawn  from  the  reservoir  H,  below ;  and,  when 
it  is  pushed  down,  this  water  is  forced  into  the  large  cylinder, 
through  the  pipe  K.  There  is  a  valve  in  this  tube  which 
prevents  the  water  from  returning,  so  that  each  stroke  of  the 
small  piston  pushes  an  additional  quantity  of  water  into  the 
larger  cylinder.  By  this  means  the  large  piston  is  pushed 
up  against  the  body  to  be  pressed. 

To  calculate  the  Pressure  exerted  by  the  large  piston, 
we  must  remember  that  the  force  acting  upon  the  piston  in 
A  will  be  exerted  upon  every  equal  amount  of  surface  in  B. 
To  illustrate  this,  suppose  the  area  of  the  large  piston  to  be 
ten  times  the  area  of  the  small  one ;  then  one  pound  at  A 
will  produce  a  pressure  of  ten  pounds  at  P. 

By  increasing  the  size  of  the  large  cylinder,  and  diminish- 
ing the  size  of  the  small  one,  the  pressure  exerted  by  a  given 
power  is  increased  proportionally.  The  weight  of  a  man's 
hand  may  thus  be  made  to  lift  a  ship  with  all  its  cargo. 
The  only  limit  to  the  increase  of  power  is  the  strength  of  the 
material  of  which  the  machine  is  made. 


SECTION   V. 
ON  THE  PROPERTIES  OF  GASEOUS  BODIES. 

17.  The  most  characteristic  properties  of  gases  are  Com- 
pressibility and  Expansibility.  Besides  these,  gases  possess 
other  properties  common  to  all  forms  of  matter,  among  which 
we  notice  Elasticity,  Weight,  and  Mobility. 


44  NATURAL   PHILOSOPHY. 

Compressibility.  —  The  compressibility  of  air  is  prettily 
shown  by  the  apparatus  represented  in  Fig.  21.     It  consists 
^^          of  a  glass  tube  with  a  bulb  at  the  upper  end,  and 
with  its  lower  end  joined  to  another  glass  tube  b}'  a 
piece  of  rubber  tubing.     A  colored  liquid  fills  the 
bend,  and  stands  at  equal  heights  in  the  glass  tubes. 
Closing  the  upper  end  of  the   open  tube  with  the 
lips,  let  the  breath  be  gentl}*  blown  into  it ;  the  fluid 
will  be  seen  to  rise  in  the  other  tube,  it  may  be  a 
distance  of  several  inches. 

The  air  in  the  bulb  can  not  escape,  and  the  mo- 
tion of  the  liquid  shows  that  the  air  is  being  crowded 
into  a  smaller  space  ;  in  other  words,  that  it  is  com- 
pressible. 

Expansibility.  —  If  the  bulb  (Fig.  21)  be  warmed 
by  grasping  it  in  the  hand,  the  colored  liquid  will 
move  downward  in  the  tube.  The  air  in  the  bulb 
expands,  and  pushes  the  liquid  along. 

Or  if,  through  the  cork  of  a  small  bottle,  a 
lg'  '  glass  tube  be  passed,  at  the  upper  end  of  which  is 
a  bulb,  and  the  lower  end  of  which  reaches  down  into  the 
colored  water  contained  in  the  bottle,  the  heat  of  a  lamp- 
flame  may  be  applied  to  the  bulb.  It  will  be  noticed  that 
bubbles  of  air  escape  from  the  lower  end  of  the  tube.  The 
air  is  expanded  so  that  the  bulb  and  tube  can  no  longer  hold 
it  all. 

When  the  flame  is  withdrawn,  the  bulb  gradually  cools, 
and  the  water  rises  in  the  tube,  and  stands  at  a  certain 
height,  as  shown  in  Fig.  22.  Now  let  the  palm  of  the  hand 
be  laid  upon  the  bulb  ;  the  water  is  driven  down  the  tube 
by  the  expanding  air.  The  gentle  warmth  of  the  hand  is 
quite  sufficient  to  produce  a  very  considerable  expansion  of 
the  air. 

These  Properties  are  characteristic.  —  Solids  and 
liquids  likewise  possess  the  properties  of  compressibility  and 
expansibility  in  various  slight  degrees.  All  gaseous  bodies 


NATURAL   PHILOSOPHY. 


45 


possess  them  in  very  high  degree.     There  seems  to  be  no 

limit  to  the  expansibility  of  gases,  and  the  limit  of  com- 
pressibility  is  reached  only  when  the  gas  is  reduced 
to  the  liquid  state. 

By  combined  pressure  and  cold,  all  gases  have  been 
changed  into  liquids. 

Elasticity.  —  The  elasticity  of  air  is  beautifully 
shown  by  the  simple  apparatus  already  used  (see 
Fig.  21)  to  illustrate  the  characteristic  properties. 
Let  the  breath  be  alternately  pressed  into  and  with- 
drawn from  the  tube,  the  air  will  alternately  be  com- 
pressed, and  spring  back,  which  will  be  shown  by 
the  alternate  motion  up  and  down  of  the  liquid  in 
the  tube. 

Weight.  —  The  air  has  weight.  If  we  would 
show  it,  we  may  first  weigh  a  closed  vessel,  prop- 
erly arranged,  and  afterward  take  the  air  out  of  it, 
and  weigh  it  again  ;  the  difference  in  these  two 

weights  will  be  the  weight  of  the  air  which  the  vessel  con- 

tains. 

But  how  can  the  Air  be  taken  out  of  a  Vessel  ?  — 

To  answer  this  question,  we  must  become  acquainted  with  the 

air-pump.      A  section  of  the 

essential  parts  of  this  impor- 

tant instrument  is  represented 

in  Fig.  23.     A  cylinder,  A  B, 

is  joined  by  means  of  a  tube, 

b  e,  to  a  very  smooth  plate,  p. 

A  piston,  c,  moves  air-tight  in 

the  cylinder.     In  the  piston  is 

a  valve,  i,  which  opens  upward, 

and    another  valve    at    b   also 

opens  upward   from   the  tube 

into  the  C37linder.     The  vessel, 


taken,  is  placed  upon  the  plate. 
called  receivers. 


Fig.  23. 

from  which  the  air  is  to  be 
Such  vessels  are  usually 


46 


NATURAL  PHILOSOPHY. 


It  will  be  seen  that  when  the  piston  is  raised,  the  valve,  z, 
will  be  closed,  and  the  air  above  it  will  be  lifted  out  of  the 
top  of  the  cylinder.  A  vacuum  would  thus  be  formed  below 
the  piston,  were  it  not  for  the  expansibility  of  the  air  in  the 
receiver.  This  air  expands,  and  a  part  of  it  is  forced  through 
the  valve,  6,  into  the  cylinder.  When  the  piston  is  pushed 
down,  the  air  below  it  passes  through  the  valve,  i;  and  when 
by  a  second  stroke  the  piston  is  lifted,  this  air  is  pushed  out 
at  the  top  of  the  cylinder,  while  another  portion  from  the 


w 


Fig.  24. 

receiver  is  pressed  through  the  tube  into  the  cj'linder  below 
the  piston.  By  each  successive  stroke,  the  quantity  of  air 
in  the  receiver  is  diminished,  until,  with  a  good  instrument, 
the  quantity  left  will  be  almost  inappreciable.  It  is  quite 
evident,  however,  that  a  perfect  vacuum  can  not  be  obtained 
in  this  way.  One  form  of  this  important  instrument,  com- 
plete, is  represented  in  Fig.  24. 

To  weigh  Air.  —  We  may  now  attend  to  the  process  of 
weighing   air.     A   hollow  glass  globe,  with  a  stop-cock,  is 


NATURAL   PHILOSOPHY. 


47 


hung  from  one  pan  of  a  delicate  balance,  and  its  weight 
carefuQy  found.  It  is  then  screwed  to  the  opening  in  the 
plate  of  the  air-pump,  and  the  air  is  exhausted.  The  stop- 
cock is  then  closed  to  prevent  the  air  from  returning  into  the 
globe,  which  is  then  taken  from  the  pump,  and  weighed.  It 


Fig.  25. 

Is  found  to  weigh  less  than  before,  and  the  difference  must 
be  the  weight  of  the  air  which  has  been  taken  out.  At  the 
ordinary  temperature  of  air,  one  hundred  cubic  inches  weigh 
about  thirty-one  grains. 

Mobility.  —  The  molecules  of  air  and  other  gases  move 
among   themselves  with   the   most   perfect  freedom.     Their 


48  NATURAL   PHILOSOPHY. 

mobility  exceeds  that  of  liquids,  because  there  is  no  cohesion 
at  all  to  be  overcome  in  them. 

Pascal's  law  and  the  principle  of  Archimedes  are  therefore 
as  applicable  to  gases  as  the}'  are  to  liquids. 

The  Ascent  of  a  Balloon  is  an  exhibition  of  the  principle 
of  Archimedes.  The  balloon  is  filled  with  coal-gas  or  hydro- 
gen, and  it  is  lighter  than  an  equal  volume  of  air.  It  is 
therefore  lifted  by  a  pressure  equal  to  the  difference  between 
the  weight  of  the  balloon  with  its  contents,  and  that  of  an 
equal  volume  of  air. 

Absolute  Weight.  —  Bodies  show  less  than  their  real 
weight  when  weighed  in  air.  The}'  lose  an  amount  equal  to 
the  weight  of  an  equal  volume  of  air.  To  obtain  their  true 
weights,  bodies  must  be  weighed  in  vacuo. 


SECTION  VI. 

ON  ATMOSPHERIC  PRESSURE. 

18.  The  atmosphere  exerts  pressure  in  all  directions. 
This  pressure  is  about  fifteen  pounds  upon  every  square  inch 
of  surface.  (G.  156,  157  ;  A.  423,  424,  426). 

The  Atmosphere  exerts  Pressure.  —  Since  every  one 
hundred  cubic  inches  of  air  weigh  about  thirty-one  grains,  it 
is  clear  that  the  atmosphere  must  be  exerting  considerable 
pressure  upon  the  surfaces  of  all  bodies  on  which  it  rests. 

This  Pressure  may  be  shown.  —  Take  a  glass  tube  of 
convenient  length,  open  at  both  ends,  and  insert  one  end  in 
a  vessel  of  colored  water.  Apply  the  lips  to  the  other  end, 
and,  as  the  air  is  drawn  out  at  the  top,  the  water  will  be 
seen  to  rise  rapidly  in  the  tube.  What  pushes  the  water 
up?  The  ancients  called  it  "Nature's  abhorrence  of  a 
vacuum  : ' '  many  at  the  present  day  are  content  to  say  that 
it  is  "sucked  up."  But  let  it  be  remembered  that  matter 
never  moves  unless  it  is  forced  to  move,  and  that  the  forces 


NATURAL   PHILOSOPHY. 


49 


of  abhorrence  and  suction  are  simply  fictions.  The  only 
force  acting  upon  the  water  is  the  weight  of  the  air  resting 
upon  its  surface  in  the  vessel.  This  downward  pressure 
pushes  the  water  under  the  lower  end  and  upward  into  the 
tube. 

It  may  be  shown  in  another  Way.  —  A  more  beautiful 
experiment  consists  in  causing  the  pressure  of  the  air  to  pro- 


Fig.  26. 

duce  a  fountain  playing  in  a  vacuum.  A  tall  glass  receiver 
(Fig.  26) ,  closed  at  the  bottom,  has  a  stop-cock  from  which 
a  tube  extends  upward  a  little  way  into  the  interior.  This 
receiver  is  first  exhausted  by  an  air-pump,  then  fixed  upon 
its  base,  and  placed  standing  in  a  vessel  of  water ;  the  stop- 
cock is  opened,  when  instantly  the  water  leaps  to  the  top  of 
the  receiver,  and  a  beautiful  fountain  continues  to  play  until 
the  jet-pipe  is  covered  by  the  falling  water. 


50 


NATURAL   PHILOSOPHY. 


The  Pressure  is  in  all  Directions.  —  An  experiment 
easily  tried  will  show  that  the  air  is  pressing  equally  in  all 
directions.  Stretch  a  piece  of  caoutchouc,  or  thin  India-rub- 
ber, over  the  large  end  of  a  lamp-chimney,  and  firmly  fasten  it 
by  winding  a  cord  around  it.  Apply  the  mouth  to  the  other 
end  of  the  tube,  and  draw  the  air  out.  The  pressure  of  the 
air  pushes  the  rubber  into  the  tube.  Hold  the  tube  so  that 
the  caoutchouc  shall  be  above,  or  below,  or 
side  wise  in  an}-  direction,  and  in  all  direc- 
tions alike  the  rubber  will  be  pushed  into 
the  tube. 

The  Pressure  is  fifteen  Pounds  to 
the  square  Inch.  —  If  the  air  should  be  all 
taken  out  of  our  tubes  used  in  the  foregoing 
experiments,  to  show  that  the  atmosphere 
exerts  pressure,  the  water  would  entirely  fill 
them ;  and  it  is  clear  that  the  pressure  of 
the  atmosphere  must  at  least  equal  the 
weight  of  the  water  which  it  lifts  into  the 
tube.  How  much  farther  the  water  would 
rise  if  the  tube  were  long  enough,  these 
experiments  have  not  told. 

A  heavier  liquid  will  not  be  lifted  as  high 
as  water,  and  will  be  more  convenient  for  ex- 
periment. Mercur}r  is  a  liquid  metal  about 
thirteen  and  a  half  times  as  heavy  as  water, 
and  it  is  found  that  the  air  will  sustain  a 
column  of  mercuiy  about  thirty  inches  high. 
The  experiment  is  conducted  as  follows : 
Take  a  glass  tube  more  than  thirty  inches  long,  closed  at  one 
end,  and  fill  it  with  mercury.  Close  the  open  end  with  the 
finger,  and  invert  the  tube.  Next  place  the  open  end  in  a 
dish  of  mercurj7,  and  withdraw  the  finger.  It  will  be  seen 
that  the  top  of  the  column  of  mercury  in  the  tube  is  only 
about  thirty  inches  above  the  surface  of  the  mercury  in  the 
dish.  (See  Fig.  27.)  The  space  above  the  mercury  in  the 


Fig.  27. 


NATURAL   PHILOSOPHY.  51 

tube  must  be  a  vacuum.  The  experiment  was  first  made 
by  Torricelli,  and  this  vacuum  is  called  the  TORRICELLIAN 
VACUUM. 

Now,  the  pressure  of  the  atmosphere  just  balances  the 
weight  of  this  column  of  mercury.  But  the  weight  of  a 
column  of  mercury  thirty  inches  high,  the  area  of  its  base 
being  one  square  inch,  is  fifteen  pounds.  The  downward 
pressure  of  the  atmosphere  is  therefore  fifteen  pounds  to  the 
square  inch  of  surface  on  which  it  rests. 

A  Unit  of  Pressure.  —  Any  pressure  of  fifteen  pounds  to 
a  square  inch  of  surface  is  called  a  pressure  of  ONE  ATMOS- 
PHERE. Heavy  pressures  are  measured  by  this  unit.  A 
pressure  of  "  four  atmospheres  "  is  a  pressure  of  4  x  15  =  60 
pounds  to  a  square  inch. 

At  a  temperature  of  140°  C.  below  zero,  oxygen  gas  under 
a  pressure  of  320  atmospheres  becomes  a  colorless  liquid. 
What  is  this  pressure  in  pounds  ? 

The  Kinetic  Theory  of  Gases.  —  It  is  believed  that  the 
distances  between  the  molecules  of  a  gas  are  very  many  times 
greater  than  the  diameters  of  the  molecules  themselves. 
Within  these  spaces  the  little  molecules  are  darting  about  in 
all  directions  ;  but  each  one  moves  in  a  straight  line  until  it 
strikes  a  neighboring  molecule,  or  the  side  of  the  vessel  in 
which  the  gas  is  held.  On  striking  another,  each  molecule 
bounds  away  in  another  straight  line  until  its  course  is  again 
changed  by  another  collision. 

Pressure  is  the  Energy  of  these  Blows.  —  It  is  easy  to 
see,  that,  if  this  theory  is  true,  the  molecules  of  air  must  be 
continually  pounding  against  the  walls  of  the  vessel  which 
contains  it ;  or,  indeed,  against  every  thing  which  it  touches. 
Every  little  blow  exerts  a  little  pressure,  and  such  a  multi- 
tude of  swift  blows  is  a  constant  pressure.  Indeed,  we  be- 
lieve that  the  pressure  of  air  is  nothing  more  than  the  energy 
of  these  molecular  blows. 

The  Radiometer.  —  In  the  radiometer  of  Crookes  (Fig. 
28)  this  molecular  energy  actually  turns  a  little  wheel.  The 


52 


NATURAL  PHILOSOPHY. 


radiometer  is  a  small  glass  globe  with  a  very  light  vane  resting 
on  a  pivot  in  the  center.  Each  one  of  the  four  arms  of  the  vane 
carries  a  disk  of  aluminum  which  is  white 
on  one  side  and  black  on  the  other.  The 
air  in  the  globe  is  exhausted  to  a  very  per- 
fect vacuum.  Of  course  there  are  then  so 
few  molecules,  that  the}'  are  able  to  fly  in 
straight  lines  much  farther  before  their 
path  is  changed  b}r  collision  with  one  an- 
other. 

Now  the  sunbeam,  or  a  candle-flame, 
will  heat  the  black  faces  of  the  disks  more 
than  the  white  ones,  and  will  make  the 
vane  whirl  in  a  surprising  manner,  by  thus 
increasing  the  energy  of  the  molecular 
motion  against  the  black  faces. 

19.  The  principle  of  atmospheric  press- 
ure is  applied  in  the  construction  of  many 
very  useful  instruments.     We  will  notice 
the   Barometer,   the   Common   Pump,  the 
Forcing  Pump,  and  the  Siphon. 


Fig.  28. 


I. —THE   BAROMETER. 

The  barometer-column  always  indicates  the  pressure  of  the 
atmosphere.  But  the  pressure  of  the  atmosphere  depends 
upon  — 

1st,  Its  height. 

2d,  The  amount  of  water- vapor  in  it.     (G.  162-167.) 

The  Barometer.  —  If  the  apparatus  used  to  determine 
the  pressure  of  the  atmosphere  (see  Fig.  27)  is  inclosed  for 
protection  in  a  frame  of  metal  or  wood,  with  a  graduated  scale 
attached  to  measure  the  height  of  the  column  of  mercuiy, 
it  forms  the  instrument  so  well  known  as  the  BAROMETER. 

Shows  the  Pressure  of  the  Atmosphere.  —  The  press- 
ure of  the  atmosphere  is  not  alwa}Ts  the  same.  When  it  is 


NATURAL   PHILOSOPHY. 


53 


less  than  fifteen  pounds  to  the  inch,  the  column  of  mercuiy 
will  be  lower  than  thirty  inches,  and,  when  greater,  the  col- 
umn will  be  higher :  indeed,  the  height  of  the  column  will 
vary  in  exact  proportion  to  every  change  in  the  pressure  of 
the  air  which  supports  it. 

If  the  top  of  the  mercury  stands  at  28  on  the  scale,  the 
pressure  of  the  atmosphere  is  f f  x  15  pounds  to  the  inch, 
nearly. 

A  Correction  necessary.  —  We  say  nearly  in  this  ex- 
ample, because  the  number  on  the  scale  at  the  top  of  the 
mercury  column  does  not  show  exactly  the  true  height.  For 
we  should  notice  that  when  the  mercury  sinks  in  the  tube, 
it  must  rise  in  the  cistern,  so  that  the  column  must  shorten 
at  both  ends.  The  figures  on  the  scale,  however,  only  show 
the  change  which  takes  place  at  the  top  :  they  fail  to  tell  the 
true  height  of  the  column. 

Made  by  Fortin's  Cistern.  —  This  error  is  avoided  in 
what  is  called  Fortin's  barometer,  by  means  of  a  cistern  with 
a  flexible  bottom.  (See  Fig.  29.)  The  bottom  of  this  cis- 
tern is  made  of  deer-skin,  and  rests  upon  the 
end  of  the  screw  C,  by  which  it  may  be  lowered 
or  lifted.  An  ivory  pointer,  A,  is  fastened  to 
the  top  of  the  cistern,  and  its  lower  end  is  the 
point  from  which  the  distances  are  measured  on 
the  scale  which  shows  the  height  of  mercury  in 
the  tube.  If  the  surface  of  the  liquid  in  the  cis- 
tern just  touches  this  point,  then  the  figures  on 
the  scale  show  the  true  height  of  the  column, 
which  indicates  the  pressure  of  the  atmosphere. 

The  Pressure  of  the  Atmosphere  depends 
upon  its  Height. — When  we  go  up  a  mountain- 
side, we  leave  a  part  of  the  atmosphere  below 
us,  and  of  course  the  height  of  the  column  above  us  is  less. 
Hence  the  weight  of  the  atmosphere  will  vary  with  the  alti- 
tude of  the  place  where  the  observation  is  made,  and  on 
this  account  the  height  of  the  barometer  column  will  be  differ- 
ent at  different  distances  above  the  sea-level. 


Fig.  29. 


54  NATURAL  PHILOSOPHY. 

To  Measure  Heights  of  Mountains.  —  Upon  this  princi- 
ple the  barometer  is  used  to  measure  the  heights  of  mountains. 

If  the  density  of  the  atmosphere  were  uniform,  the  fall  of 
the  mercury  would  be  in  the  exact  ratio  of  the  distances  up- 
ward ;  and,  knowing  the  height  required  to  make  the  mercury 
fall  one-tenth  of  an  inch,  this,  multiplied  by  the  number  of 
tenths  through  which  it  is  observed  to  sink,  would  tell  the 
height  of  the  mountain.  The  truth  is,  however,  that  the 
density  of  the  air  rapidly  diminishes  as  we  ascend.  Tempera- 
ture, too,  affects  its  pressure.  In  spite  of  these  difficulties, 
tables  have  been  constructed  by  which  the  height  of  a  place 
above  the  sea-level  may  be  calculated  by  observing  the  height 
of  the  barometer-column  and  the  temperature  of  the  atmos- 
phere. 

Pressure  depends  also  upon  the  Amount  of  Water- 
Vapor  present. — Mixed  with  the  air,  at  all  times,  are  con- 
siderable quantities  of  invisible  vapor  of  water.  If  the  at- 
mosphere were  pure  dry  air  alone,  it  would  exert  a  certain 
pressure  ;  if  it  consisted  wholly  of  water-vapor,  it  would  exert 
a  different  amount  of  pressure  :  it  does  consist  of  a  mixture 
of  these  two  gases,  and  the  pressure  it  exerts  is  the  sum  of 
the  pressures  they  would  separately  exert. 

It  follows  that  the  atmospheric  pressure  will  be  greatest 
when  there  is  the  greatest  quantity  of  water-vapor  in  the  air : 
the  barometer-column  will  then  rise.  But  let  this  vapor  be 
condensed  into  clouds,  and  it  will  have  but  little  force  of 
elasticity,  and  will  exert  but  a  small  fraction  of  its  former 
pressure :  hence  the  barometer-column  will  stand  lower  in 
cloudy  weather. 

To  predict  Weather  Changes.  —  On  this  principle  the 
barometer  is  used  to  indicate  changes  in  the  weather.  A 
rising  column  indicates  fair  weather;  a  falling  column  indi- 
cates foul  weather. 

This  rule  is  to  a  great  extent  reliable.  Others  are  added 
by  different  observers,  but  they  must  be  taken  with  consider- 
able allowance. 


NATURAL  PHILOSOPHY. 


II. —THE   COMMON  PUMP. 

D'-scriptioii.  —  This  instrument,  as  general!}' made,  con- 
sists of  two  cylinders  or  barrels,  A  and  B,  Fig.  30,  with  a 
valve,  S,  at  their  junction,  opening  up- 
ward. In  the  upper  barrel  is  a  piston, 
P,  in  which  is  a  valve,  O,  also  opening 
upward.  The*  piston  is  moved  by 
means  of  the  handle  H,  and  the  water 
may  flow  from  the  spout  C. 

Explanation.  —  When  the  piston  is 
lifted,  the  air  above  it  will  be  lifted  out 
of  the  barrel.  A  partial  vacuum  will 
thus  be  formed  below  the  piston,  and 
the  pressure  of  the  air  upon  the  surface 
of  the  water  in  the  well  will  push  the 
ftrater  up  the  barrel  A,  through  the 
valve  S,  into  the  barrel  B.  When 
the  piston  goes  down,  the  valve  S  will 
"lose,  and  prevent  the  return  of  the 
water  to  the  well.  The  valve  in  the 
piston  will  be  opened,  and  the  water 
will  pass  through  it.  When  the  piston 
is  again  lifted,  the  water  now  above  it 
will  be  lifted  to  the  spout,  while  the 
atmospheric  pressure  will  force  another 
portion  into  the  barrel  below  the  piston. 


Fig.  30. 


Limit  of  Height.  ^—  At  the  sea-level  the  pressure  of  the 
air  wall  sustain  a  column  of  mercury  about  thirty  inches 
high.  Since  mercury  is,  at  ordinary  temperature,  about  13| 
times  heavier  than  water,  the  same  force  will  lift  a  column  of 
water  131  times  as  high  :  13|  X  30  =  405  ;  405  in.  =  33| 
feet.  The  atmosphere  can  not  lift  water  in  the  common 
pump  to  a  greater  height  than  this,  even  at  the  level  of  the 
sea.  In  practice  the  valve  S  must  be  less  than  33J  feet 
above  the  water. 


56 


NATUBAL  PHILOSOPHY, 


III.— THE  FORCING  PUMP. 

Description. — In   the   forcing  pump  the  piston  has  ho 
valve,  but  from  near  the  bottom  of  the  upper  barrel  there  is 
a  tube  passing  to  an  air-chamber,  with 
a  valve  opening  into  the  chamber.     A 
section  of  this  instrument  is  represented 
in   Fig.   31.     Reaching  from   near  the 
bottom  of  the   air-chamber,  I  K,  is  a 
tube,  L  M,  which  extends  to  any  place 
K  at  which  the  water  is  to  be  delivered. 

Explanation.  —  Now,  when  the  sol- 
id piston  P  is  raised,  water  is  pressed 
through  the  valve  E,  into  the  barrel  B. 
When  the  piston  is  pushed  down  again, 
the  water  is  driven  through  the  tube 
into  the  air-chamber,  and  compresses 
the  air  in  it.  B}'  eveiy  stroke,  the  water 

accumulates  in  the  chamber,  and  the  air  is  more  and  more 
compressed.  The  pressure  of  this  condensed  air  upon  the 
water  in  the  chamber  pushes  it  up  through  the  tube  L  M, 
to  the  place  where  it  is  desired.  Without  the  air-chamber, 
the  water  wrould  issue  from  the  pipe  in  jets  :  with  the  cham- 
ber, the  water  issues  in  a  steady  stream. 


IY.  —  THE   SIPHON. 

Description.  —  The  siphon  is  an  instrument  b}r  which 
liquids  may  be  transferred  from  one  vessel  to  another,  by  at- 
mospheric pressure.  It  consists  of  a  bent  tube,  one  arm  of 
which  is  longer  than  the  other.  In  Fig.  32  the  siphon  in 
operation  is  shown.  Having  been  first  filled  with  water,  its 
short  arm  is  inserted  in  the  water  to  be  transferred  from  the 
vessel  C,  and  it  is  then  found  that  the  water  will  flow  stead- 
ily until  the  lower  end  of  the  short  arm  is  left  uncovered, 
or,  in  other  cases,  until  the  water  in  the  two  vessels  stands 
at  the  same  level. 


NATURAL  PHILOSOPHY. 


57 


Explanation.  —  The  downward  pressure  of  the  air  at 
C  is  partly  balanced  by  the  weight  of  the  column  of  water, 
C  D,  in  the  short  arm  of  the 
tube ;  the  excess  of  pressure 
will  tend  to  push  the  water 
over  through  the  bend  toward 
B.  On  the  other  hand,  the 
atmospheric  pressure  at  B  is 
parti}-  balanced  by  the  pressure 
of  the  water  in  the  long  arm, 
which  is  equal  to  the  weight  of 
a  column  A  B  ;  the  excess  will 
tend  to  push  the  water  back 
through  the  bend  toward  C. 
It  is  clear  that  the  pressure  of 
air,  minus  the  weight  of  the  shorter  column  of  water,  is  more 
than  the  same  pressure,  minus  the  weight  of  the  longer 
column,  and  hence  that  a  greater  force  will  be  exerted  to 
push  the  water  from  C  toward  B,  than  from  B  toward  C  :  the 
liquid  will  flow  in  the  direction  of  the  greater  force,  up  the 
short  arm,  over  the  bend,  M,  and  out  at  B. 


Fig.  32. 


SECTION    VII. 
ON   "THE   THREE   LAWS." 

There  are  three  fundamental  principles  which  apply  to  all 
true  gases.     They  are  known  as 

The  Law  of  Boyle  or  Harriot te, 
The  Law  of  Charles, 
The  Law  of  Avogadro. 


L— THE  LAW   OF  BOYLE. 

20.  The  volume  of  a  given  weight  of  air  will  be  inversely 
as  the  pressure  upon  it.     (G.  174,  175  ;  A.  412,  458.) 


58 


NATURAL  PHILOSOPHY. 


Volume  depends  upon  the  Pressure.  —  Press  the 
breath  into  the  open  tube  of  the  apparatus  represented  in 
Fig.  21,  and  the  liquid  flows  toward  the  bulb,  showing  that 
the  air  in  the  bulb  is  condensed.  Next  draw  the  air  out  of 
the  tube,  and  the  liquid  flows  away  from  the  bulb,  showing 
that  the  air  within  is  expanded.  The  same  quantity  of  air 
is  here  seen  to  fill  less  space  when  the  pressure  upon  it  is 
increased,  and  more  space  when  the  pressure  is  diminished. 
Plan  for  further  Experiment.  —  Now,  we  may  prove 
by  experiment,  first,  that  with  a  double 
pressure,  the  volume  will  be  just  one-half; 
and,  second,  that  with  half  the  pressure, 
the  volume  will  be  just  double. 

Pressure  greater  than  one  Atmos- 
phere.—  In  the  first  case,  we  use  a  bent 
glass  tube  (Fig.  33),  the  short  arm  being 
closed,  and  the  other,  which  should  be 
more  than  thirty  inches  long,  being  open 
at  the  top.  A  graduated  scale,  to  which 
the  tube  is  firmly  bound,  measures  inches 
from  the  bend. 

Now  let  mercury  be  poured  into  the 
tube,  until  it  fills  the  bend.  The  air 
presses  upon  the  mercury  in  the  long 
arm,  and  this  liquid  transmits  'the  same 
pressure  to  the  air  in  the  short  arm.  The 
pressure  upon  the  air  in  the  short  arm 
is,  therefore,  fifteen  pounds  to  the  square 
inch.  If  we  fill  the  long  arm  with  mer- 
cury, as  shown  in  the  figure,  to  the  height 
of  thirty  inches  above  the  level  of  the  mer- 
cury in  the  other,  we  shall  be  adding  a 
Fig.  33.  pressure  of  fifteen  pounds  to  the  inch. 

The  pressure  upon  the  air  in  the  short  arm  will  then  be 
doubled;  and  we  shall  discover  that  the  mercury  has  risen, 
crowding  the  air  before  it,  and  stands  at  A,  the  air  having 
just  half  its  original  volume. 


NATURAL   PHILOSOPHY. 


59 


Pressures  less  than  one  Atmosphere.  —  In  the  second 
case,  we  take  a  glass  tube  (A  B,  Fig.  34),  about  twenty- 
five  inches  long,  and  open  at  both  ends.  Let  three  narrow 
bands  of  paper  be  pasted  upon  it,  the  first  at  a  distance  of 
three  inches  from  the  top,  the  second  six  inches  from  the  top, 
and  the  third  fifteen  inches  from  the  second. 
Let  another  larger  tube,  D,  about  thirty 
inches  long,  be  nearly  filled  with  mercuiy. 
Insert  the  end,  A,  of  the  small  tube,  in  this 
mercury,  and  push  it  down  until  the  upper 
mark  (3)  is  at  the  level  of  the  mercury. 
Now,  clasping  the  finger  tightly  over  the  end 
B,  thus  inclosing  three  inches  of  air  in  the 
tube,  lift  it  until  the  third  mark  is  brought 
up  to  the  top  of  the  mercur}-.  The  air  will 
be  found  to  fill  the  space  of  six  inches. 

Before  the  tube  was  lifted,  the  whole  press- 
ure of  the  atmosphere,  fifteen  pounds  to  the 
inch,  was  exerted  upon  the  air  within :  after 
the  tube  was  lifted,  the  atmosphere  sustained 
a  column  of  mercuiy  fifteen  inches  high.  To 
do  this,  required  half  the  pressure  it  can 
exert :  the  other  half  was  exerted  upon  the 
six  inches  of  air  above  the  mercury.  We 
thus  show  that  with  half  the  pressure  the 
volume  will  be  just  double. 

What  is  true  in  both  Cases  ?  —  In  these  two  experiments 
we  find  that  the  volume  of  a  given  weight  of  air  is  inversely 
as  the  pressure  upon  it;  and  repeated  experiment  confirms 
the  inference  that  the  same  principle  holds  true  for  other 
pressures. 

This  law  was  discovered  independently  by  Robert  Boyle 
in  England,  and  the  Abbe  Marriotte  in  France. 

The  Density  of  the  Atmosphere. — When  a  given 
weight  of  air  is  crowded  into  one-half  its  original  volume,  it 
must  be  twice  as  dense  ;  and,  when  expanded  into  double  its 


Fig.  34. 


60  NATURAL    PHILOSOPHY. 

first  volume,  it  can  only  be  half  as  dense.  The  density  of 
air  will  therefore  be  exactly  in  proportion  to  the  pressure 
upon  it.  So  the  atmosphere,  where  its  own  pressure  is  great- 
est, will  be  most  dense. 

Is  greatest  at  tlie  Surface  of  the  Earth The  at- 
mosphere in  contact  with  the  earth  is  pressed  upon  by  all 
the  air  above,  even  to  the  top  of  the  atmosphere.  At  a  dis- 
tance above  the  earth,  the  atmosphere  receives  less  pressure, 
because  there  is  less  air  above  to  exert  it.  The  density 
being  greatest  where  the  pressure  is  greatest,  the  air  at  the 
surface  must  be  more  dense  than  the  portions  above.  The 
air  is  much  less  dense  at  the  top  of  a  high  mountain  than  at 
its  base. 

II. —THE  LAW   OF   CHARLES. 

21.  The  volume  of  a  given  weight  of  air  will  be  greater 
as  its  temperature  is  higher.  It  expands  ¥JT  of  its  bulk  at 
32°  for  every  additional  degree  Fahrenheit,  or  ^^  of  its 
bulk  at  0°  for  each  degree  Centigrade. 

Charles's  law  declares  that  the  volume  of  a  given  weight 
of  gas  is  directly  as  its  absolute  temperature. 

Heat  increases  the  Volume  of  Air.  —  Let  the  palm 
of  the  hand  be  laid  upon  the  bulb  (Fig.  22),  and  the  fluid  in 
the  tube  descends,  because  the  air  in  the  bulb  expands.  Pour 
cold  water  upon  the  bulb,  and  the  fluid  ascends,  because  the 
air  above  it  is  condensed.  Apply  the  heat  of  the  lamp-flame 
to  the  bulb,  and  the  water  in  the  tube  will  be  quite  driven 
out  at  the  bottom :  let  it  cool  again,  and  the  water  rises  to 
its  former  height.  These  experiments  show  that  the  addition 
of  heat  expands  air,  and  that  its  withdrawal  contracts  it. 

At  the  Bate  of  T^y  its  Bulk  for  each  Degree.  —  The 
expansion  of  air  and  other  gases,  by  heat,  is  uniform.  One 
degree  of  heat  when  the  temperature  is  low  produces  the 
same  expansion  as  one  degree  when  the  temperature  is  high. 
If  we  have  491  cubic  inches  at  a  temperature  of  32°,  it  will 
become  492  cubic  inches  if  heated  one  degree,  making  its 


NATURAL   PHILOSOPHY.  61 


temperature  33°.  In  other  words,  it  expands  ^-Jy  of  the  vol- 
ume at  32°,  for  each  additional  degree  of  heat  applied. 

If  the  Centigrade  scale  of  temperature  be  used,  then  the 
illustration  is  as  follows  :  273  cubic  inches  of  gas  at  0°  will 
become  274  cubic  inches  if  heated  to  1°.  That  is  to  say,  it 
expands  ^  3-  of  its  volume  at  0°  for  each  additional  degree. 

One  hundred  cubic  inches  of  air  at  32°  F.  will  be  expanded 
at  60°  F.  to  be  100  +  -?fc  X  100  =  105.7  cubic  inches. 

The  Effect  of  Cooling-  --  Conversely  each  degree  of  heat 
taken  awajr  from  a  gas,  beginning  at  0°  C.  or  32°  F.,  will 
reduce  its  volume  at  the  same  rates.  273  cubic  inches  at 
0°  C.  will  be  272  cubic  inches  at  —  1°  C.,  and  271  cubic  inches 
at  —2°  C.  The  gas  would  go  on  losing  ^^  of  its  volume 
for  each  degree  of  lower  temperature.  Then 

How  many  Deg  rees  can  be  withdrawn  ?  —  Not  more 
than  273,  because  it  would  be  impossible  for  the  gas  to  con- 
tract more  than  f^-f  of  its  volume.  If  the  law  holds  good 
at  such  low  temperature,  then  at  —273°  C.  the  volume  of  a 
gas  would  be  infinitely  small,  and  it  would  be  impossible  to 
conceive  it  airy  colder. 

Absolute  Temperature.  —  This  point  on  the  Centigrade 
s^-ale,  —273°,  is  called  the  absolute  zero,  and  temperatures 
measured  from  this  point  are  called  the  absolute  temperatures. 

Absolute  temperatures  are  obtained  by  adding  273  to  the 
temperature  on  the  Centigrade  scale.  Thus  60°  is  333°  on 
the  absolute  scale,  and  —40°  is  233.° 

The  Law  of  Charles  declares  that  the  volume  of  a  given 
weight  of  gas,  the  pressure  being  unchanged,  will  vary  directly 
as  the  absolute  temperature. 

III.  —THE  LAW   OF   AVOGADRO. 

22.  Equal  volumes  of  all  gases,  at  the  same  temperature 
and  pressure,  contain  the  same  number  of  molecules. 

Illustration.  —  It  is  believed  that  there  are  just  as  many 
molecules  in  a  cubic  inch  of  oxj'gen  as  there  are  in  a  cubic 


62  NAtUHAL   PHILOSOPHY. 

inch  of  hydrogen,   when   these   gases   are    under  the  same 
pressure  and*  at  the  same  temperature. 

The  prftdf  of  this  law  is  found  in  the  stud}'  of  mathemat- 
ical ph}'sics  and  of  the  science  of  chemistry.  We  must 
therefore  omit  the  demonstration  now ;  but  the  law  itself 
should  be  remembered  with  those  of  Boyle  and  Charles, 
because  these  three  laws  together  define  tho  truly  gaseous 
condition  of  matter. 


SECTION   VIII. 

REVIEW. 
I. —SUMMARY   OF  PRINCIPLES. 

The  solid,  liquid,  and  gaseous  conditions  depend  on  the 
relative  strength  of  attraction  and  repulsion  between  the 
molecules  of  the  body.  Hence, 

Hardness,  tenacit}',  malleability,  ductilit}',  and  crystalline 
form  are  properties  of  solids  only  ;  while 

Mobility  is  the  characteristic  property  of  liquids,  and 

Compressibility  and  expansibility  are  the  characteristic 
properties  of  gases. 

The  pressure  of  a  liquid  at  rest  is  due  to  gravitation,  and 
is  exerted  equally  in  all  directions.  For  this  reason, 

The  surface  of  water  at  rest  must  be  level.  The  liquid 
will  always  rise  to  the  same  height  in  all  tubes  or  reservoirs 
which  communicate  with  one  another. 

The  pressure  of  a  liquid  on  the  base  of  the  vessel  contain- 
ing it  depends  upon  two  things  only,  —  the  area  of  the  base, 
and  the  height  of  the  liquid  above  the  base.  It  is  equal  to 
the  weight  of  a  column  as  large  as  the  base  of  the  vessel 
and  as  high  as  the  surface  of  the  liquid. 

A  bod}'  immersed  in  fluid,  either  liquid  or  gaseous,  is 
pressed  both  upward  and  downward ;  but  the  upward  press- 
ure is  the  greater.  Hence  a 'body  loses  weight  when  im- 
mersed, and  its  loss  is  just  equal  to  the  weight  of  the  fluid 
it  displaces. 


NATURAL   PHILOSOPHY.  -       68 

A  fluid,  either  liquid  or  gaseous,  transmits  external  press- 
ure in  every  direction,  and  allows  it  to  act -with  the  same 
energy  on  eveiy  equal  amount  of  surface.  »  * 

II.  —  SUMMARY  OF  TOPICS. 

8.  The  molecular  forces.  —  Illustrated  in  natural  changes 
in  condition.  —  In  artificial  changes. 

9.  Hardness.  — Tenacit}r.  — Malleability.  —  Ductility.  — 
Cr}'stalline  form.  —  These  properties  characteristic  of  solids. 

10.  Elasticity  of  liquids.  —  Attraction  and  repulsion  nearly 
equal.  —  Mobility.  —  Characteristic  property. 

11.  Liquids  press  in  all  directions. — Equall}'. — The  sur- 
face at  rest  must  be  level.  — Level  surface  convex. 

12.  Water  in  pipes  rises  as  high  as  its  source.  — The  sup- 
ply of  water  to  cities.  — Springs.  — Artesian  wells. 

13.  Pressure  independent  of  the  shape  of  the  vessel.  — It 
depends  on  the  depth  of  the  liquid.  —  On  the  area  of  the 
base.  —  To  calculate  the  pressure.  —  Against  any  surface. 

14.  Bodies  immersed  are  pressed  upward. — With  force 
equal  to  the  weight  of  fluid  displaced. — The  solid  lighter 
than  water.  —  The  solid  heavier  than  water. 

15.  Specific  gravity.  —  Of  gases.  —  Of  liquids.  —  By  di- 
rect weighing.  — B}'  the  hydrometer.  — By  the  use  of  a  bulb. 

—  Of  solids. — Heavier  than  water.  —  Describe  the  experi- 
ment. —  Lighter  than  water.  —  Table. 

1C.  The  equal  transmission  of  pressure.  — Experiment.  — 
The  shape  of  the  vessel  makes  no  difference. — The  hydro- 
static press. 

17.  Of  the  properties  of  gases.  —  Compressibilit}'.  —  Ex- 
pansibilitj'.  —  These    properties    characteristic.  —  Elasticity. 

—  Weight.  —  The  air-pump.  —  To  weigh  air.  —  Mobility.  — 
Ascent  of  a  balloon.  — Absolute  weight. 

18.  The  atmosphere  exerts  pressure.  —  Shown  loy  experi- 
ment.—  In    all   directions. — About    fifteen    pounds    to    the 
square  inch. — Unit  of  pressure.  —  The   Kinetic  theory. — 
The  radiometer. 


64  NATURAL   PHILOSOPHY. 

19.  The  barometer. — Shows  the  pressure  of  the  atmos- 
phere.—  Correction  needed. — Made  by  Fortin's  cistern. — 
The  pressure  of  the  atmosphere  depends  upon  its  height.  — 
Measurement  of  mountains.  —  Upon  the   amount  of  water- 
vapor  it  contains.  —  To  predict  changes  in  the  weather. — 
The  common  pump.  — The  forcing-pump.  — The  siphon. 

20.  Volume  of  gas  depends  on  pressure. — Plan  for  experi- 
ment.—  Pressure  greater  than  one  atmosphere. — Pressure 
less  than  an  atmosphere.  — Law  deduced.  — Densit}'  of  the 
atmosphere. — Density  greatest  at  surface  of  the  earth. 

21.  Heat  increases  the  volume  of  air. — At  the  rate  of 
4^Y  of  its  bulk  for  each  degree. — The  effect  of  cooling. — 
How  many  degrees  can  be  withdrawn  ?  —  Absolute  tempera- 
ture.—  Law  of  Charles. 

22.  Law  of  Avogadro. —  Illustration. 

III.  —  PROBLEMS. 
Problems  illustrating  the  Laws  of  Hydrostatics. 

1.  A  C3*lindrieal  vessel,  whose  base  is  5  square  feet,  is   10 
feet  high.     It  is  filled  with  water.     What  pressure  is  exerted 
upon  the  base?  Ans.  3125  pounds. 

2.  If  the  bottom  of  a  vessel  has  an  area  of  72   square 
inches,  and  its  top  an  area  of  96   square  inches,  and  it  is  9 
inches  high,  what  pressure  will  be  exerted  on  the  bottom 
when  the  vessel  is  full  of  water?        Ans.  23.43+  pounds. 

3.  Two  vessels  with  equal  bases  are  filled  with  water,  one 
to  a  height  of  9  inches,  the  other  to  a  height  of  27  inches. 
How  man}'  times  more  pressure  on  the  base  in  the  last  case 
than  in  the  first?  Ans.  3. 

4.  How  much  pressure   is  exerted  against  the  side  of  a 
cubical  vessel  which   is   full   of  water,  its  height  being  18 
inches?  Ans.  105. 46 -f-  pounds. 

5.  How  much  pressure  would  be  exerted  upon   12   square 
inches  of  the  sides  of  the  vessel  when  the  middle  point  of 
this  surface  is  20  inches  below  the  top  of  the  water? 

Ans.  8.68  pounds. 


NATURAL   PHILOSOPHY.  65 

6.  How  many  cubic  inches  of  water  will  be  displaced  by 
a  piece  of  pine  wood  weighing  just  10  pounds? 

Ans.  276.48. 

7.  How  much  less  will  a  piece  of  marble  measuring  100 
cubic  inches  weigh  in  water  than  in  air?  Ans.  3.61  pounds. 

8.  The  specific  gravity  of  marble  being  2.7,  what  will  be 
the  weight  of  25  cubic  feet?  Ans.  4218.75  pounds. 

9.  How  man}'  cubic  inches  in  a  block  of  ice  that  weighs 
75  pounds?  Ans.  2229.67. 

10.  What  is  the  specific  gravity  of  flint-glass  if  a  frag- 
ment of  it  weigh,  in   air,  4320  grains,  and  in  water  3023 
grains?  Ans.  3.33. 

11.  The  specific  gravity  of  wax  is  to  be  found  from  the 
following  data :  — 

Weight  of  the  wax  in  air  ....  8  ounces. 
Weight  of  a  piece  of  lead  in  air  .  .  16  ounces. 
Weight  of  the  lead  in  water  .  .  .  .14.6  ounces. 
Weight  of  wax  and  lead  in  water  .  13.712  ounces. 

Ans.  0.9. 

12.  A  bottle  holding  1000  grains   of  water  is   found   to 
hold  only  870  grains  of  oil  of  turpentine.     What  is  the  spe- 
cific gravity  of  this  oil?  Ans.  0.87. 

13.  How  much   pressure   can   be  exerted  upon  the  large 
piston  of  a  hydrostatic  press  by  applying  fifty  pounds  to  the 
small  piston ;   the   area  of  the  small  piston  being  one-half 
square  inch,  that  of  the  large  piston  100  square  inches? 

Ans.  10000  Ibs. 

Problems  illustrating  the  Laws  of  Gaseous  Bodies. 

1.  What  is  the  weight  of  a  cubic  foot  of  air  at  ordinary 
temperature  and  pressure?  Ans.  535.68  grains. 

.  2.  What  is  the  weight  of  100  cubic  inches  of  oxygen  gas 
at  ordinary  temperature  and  pressure,  its  specific  gravity 
being  1.106?  Ans.  34.286  grains. 

3.  What  is  the  weight  of  100  cubic  inches  of  nitrogen  gas 
at  ordinary  temperature  and  pressure,  its  specific  gravity 
being  .972? 


66  NATURAL  PHILOSOPHY. 

4.  What  pressure\will  be  exerted  by  the  atmosphere  on  a 
surface  of  one  square  foot  ?  Ans.  2,160  pounds. 

5.  What  pressure  does  the  atmosphere  exert  upon  a  square 
Inch  surface  when  the  rkrometer  column  is  28  inches  trigh  ? 

Ans.  14  pounds. 

6.  How  high   a  column  of  water  would   the  atmosphere 
sustain  when  the  barometer  column  stands  at  a  height  of  28 
inches?  Ans.  31^  feet. 

7.  Suppose  100  cubic  inches  of  air  at  a  pressure  of  15 
pounds  to  the  inch  is  made  to  receive  an  additional  pressure 
of  15  pounds  to  the  inch :  what  will  be  its  volume? 

Ans.  50  cubic  inches.' 

8.  How  much  pressure  must  be  removed  from   100  cubic 
inches  of  air,  at  usual  density,  in  order  that  it  may  expand 
to  a  volume  of  200  cubic  inches  ? 

Ans.  7jj  pounds  to  the  inch. 

9.  In  the  air-chamber  of  the  forcing-pump  the  air  is  com- 
pressed into  half  its  former  bulk  ;  how  high  will  the  wrater 
be  thrown?  Ans.  33f  feet. 

10.  If  we  have  500  cubic  inches  of  air  at  32°  F.  tempera- 
ture, how  much  will  there  be  when  it  is  heated  to  a  tem- 
perature of  75°?  Ans.  543.78-f  cubic  inches. 


NATURAL  PHILOSOPHY.  .    67 


CHAPTER   III. 

OX  MOTION. 

23.  The  Fundamental  Ideas. — ATTRACTION  and  REPUL- 
SION acting  upon  masses  or  MOLECULES  of  matter  determine 
their  condition  of  rest  or  motion. 

Illustration. — The  motion  of  bodies  falling  to  the  ground 
is  due  to  the  attraction  of  gravitation.  The  motion  of  air 
in  wind  is  caused  chiefly  by  the  repulsive  power  of  heat. 
The  bullet  speeds  on  its  wa}-,  urged  by  the  repulsive  force 
of  exploding  gunpowder.  The  forces  which  produce  the 
endless  variet}'  of  motions  in  nature  are  found,  when  care- 
fully studied,  to  be  only  different  forms  of  attraction  and 
repulsion. 

SECTION   I. 
ON  MOTION  CAUSED  BY  A  SINGLE  FORCE. 

24.  There  are  three  important  principles  known  as  New- 
ton's laws  of  motion  :  — 

1st,  A  body  at  rest  will  remain  at  rest ;  or,  if  in  motion, 
it  will  move  forever  in  a  straight  line,  unless  acted  upon  by 
some  force  to  change  its  condition. 

2d,  A  given  force  will  produce  the  same  amount  of  motion, 
whether  it  act  upon  a  bod}r  at  rest  or  in  motion. 

3d,  Action  and  reaction  are  equal,  and  in  opposite  direc- 
tions. (A.  154-157,  168.) 

The  first  Law.  —  The  truth  of  the  first  law  is  seen  when 
we  remember  that  the  inertia  of  matter  forbids  that  a  body 
shall,  in  any  way,  change  its  own  condition. 


68  KATtJEAL  PHILOSOPHY. 

Then,  why  are  bodies  so  constantly  changing  their  condi- 
tion of  rest  or  motion?  We  rarely  see  a  bod}*  in  nature, 
moving  in  an  absolutely  straight  line  ?  The  reason  is  this : 
bodies  are  constantly  under  the  influence  of  forces  which  do 
change  their  condition.  A  stone  thrown  from  the  hand  would 
move  forever  in  a  straight  line,  if  it  felt  only  the  force  of  the 
hand ;  but  gravitation,  and  the  resistance  of  the  air,  compel 
it  to  move  in  a  graceful  curve  instead.  The  pleasing  variety 
of  natural  motions  is  brought  about  by  the  unceasing  action  of 
external  forces. 

The  second  Law.  —  Let  us  examine  this  law  by  means 
of  the  diagram,  Fig.  35.  If  a  ball  be  thrown  suddenly  from 

the  point  A,  hori- 

A  (^--,  ~|  B   zontall}',   it   would 

go  to  the  point  B, 
if  it  could  be  let 
alone  by  other  for- 
ces. So  likewise, 
if  it  be  dropped 
from  A,  gravitation 

—  — ^'      alone  will  cany  it 

ll'ig'  35'  to  C.     Now,  these 

separate  effects  of  the  two  forces  will  be  exactly  produced 
when  the  forces  act  together.  Suppose  the  ball  to  go 
from  A  to  B  in  one  minute,  and,  when  dropped,  to  fall  from 
A  to  C  in  the  same  time.  While  the  ball  is  moving 
toward  B,  gravitation  is  pulling  it  downward,  and  at  the  end 
of  the  minute  it  will  be  found  at  D,  having  moved  to  the 
right  a  distance  exacth*  equal  to  AB,  and  downward  through 
a  distance  exactly  equal  to  A  C  ;  so  that  the  force  of  gravi- 
tation produces  the  same  effect,  whether  it  act  upon  the  ball 
resting  at  A  or  in  motion  toward  B. 

The  third  Law.  —  If  a  table  be  struck,  the  hand  that 
strikes  it  receives  a  blow  as  well.  The  hand  acts  upon  the 
table  ;  the  table  reacts  upon  the  hand.  Attend,  now,  to  the 
following  experiment.  Two  ivory  balls  are  suspended  by 


NATURAL  PHILOSOPHY, 


69 


cords,  and  hang  in  contact  against  a  graduated  arc.  When 
the  ball  B  is  lifted  up  the  arc  to  D,  and  then  allowed  to 
swing  against  the  other, 
it  strikes  it,  and  instantly 
stops,  while  the  othefball 
takes  up  its  motion,  nnd 
goes  to  the  point  C.  The 
first  ball  acts  upon  the 
second ;  the  second  re- 
acts upon  the  first.  Now, 
if  we  notice  that  the  mo- 
tion from  D  to  B,  which  is 
stopped  by  the  reaction 
of  the  second  ball,  is  just 
equal  to  the  motion  from  A  to  C,  which  is  caused  by  the  ac- 
tion of  the  first,  it  becomes  evident  that  the  two  forces  must 
be  equal,  and  exerted  in  opposite  directions. 

It  follows  from  this  principle,  that,  when  two  bodies  come 
in  contact,  each  one  gives  and  receives  an  equal  shock. 
The  hand  which  strikes  the  table  is  itself  bruised,  and  the 
bullet  which  shatters  the  bone  is  itself  battered. 

25.  The  velocity  of  a  moving  bod}7  will  be  uniform  if  it  be 
produced  by  an  impulsive  force,  and  opposed  by  no  resist- 
ances. 

The  elements  of  motion  are  Time,  Space,  and  Velocity. 
In  uniform  motion,  the  space  is  equal  to  the  product  of  time 
multiplied  by  velocity.  (G.  25  ;  A.  105,  110.) 

Velocity.  —  Velocity,  in  a  popular  sense,  is  simpty  rapid- 
ity of  motion  ;  but  if  the  term  is  to  be  of  any  scientific 
value  it  must  be  more  definitely  applied.  Velocity  is  the 
distance  passed  over  by  a  body  in  a  unit  of  time.  The 
velocity  of  a  cannon-ball,  for  example,  may  be  two  thousand 
feet  a  second  ;  that  of  a  train  of  cars  may  be  thirty  miles  an 
hour. 

Uniform  Velocity.  —  In  uniform  velocity,  a  body  moves 


70  NATURAL  PHILOSOPHY. 

over  equal  spaces  in  equal  times.  If,  for  instance,  in  each 
of  three  successive  hours,  a  steamboat  travels  fifteen  miles, 
its  velocity  is  uniform. 

An  impulsive  Force.  —  An  impulsive  force  is  one  which, 
after  acting  for  a  time,  ceases.  The  stroke  of  a  bat, 
which  knocks  the  ball,  is  an  impulsive  force ;  so  are  the 
blows  of  a  hammer.  No  matter  how  long  a  force  may  have 
been  acting,  if  it  be  suddenly  withdrawn,  it  is  at  that  moment 
an  impulsive  force. 

Uniform  Motion  produced  by  an  Impulse.  —  If  a 
body  can  be  free  from  all  forces  but  the  impulse  which  gives 
it  motion,  its  velocity  will  be  uniform.  This  seldom  occurs. 
How  rarel}'  do  we  see  a  uniform  motion  produced  b}T  an  im- 
pulse, either  in  nature  or  in  art !  This  is  because  all  bodies 
are  under  the  influence  of  several  forces  at  once,  such  as  gravi- 
tation, friction,  and  the  resistance  of  air,  b}*  which  their 
velocities  are  changed.  The  motion  of  the  earth  on  its  axis 
is,  however,  a  sublime  example  of  uniform  motion. 

In  the  arts,  a  uniform  motion  can  be  secured  only  by  the 
constant  application  of  power.  The  impulse  which  starts  a 
train  of  cars  would  make  it  move  uniformly  if  it  did  not  meet 
with  resistances  ;  to  overcome  these,  a  constant  pressure  of 
the  steam  must  be  applied.  If  this  pressure  be  at  all  times 
just  enough  to  accomplish  that  purpose,  the  motion  of  the 
train  will  be  uniform. 

Space  equals  Time  multiplied  by  Velocity.  —  It  is 
evident  that  a  train  of  cars,  going  uniformly  at  the  rate  of 
25  miles  an  hour,  will  in  10  hours  go  250  miles.  But  we 
see  that  250  =  25  x  10,  or,  that  the  space  is  equal  to  the 
product  of  the  two  other  elements,  time  and  velocity. 

We  n,ay  express  this  principle  by  the  simple  equation,  — 

S  =  T  x  V: 

in  which  S  stands  for  Space ;  T  stands  for  Time  ;  V  stands, 
for  Velocit}'. 

Now,  if  any  two  of  these  elements  are  given,  the  third 
may  be  found  by  substituting  the  given  values  for  the  letters, 


NATUEAL  PHILOSOPHY.  71 

and  then  performing  the  operations  indicated.  For  example, 
what  is  the  velocity  of  a  bullet  which  flies  2,000  feet  in  20 
seconds,  supposing  its  velocity  uniform?  The  value  of  S  is 
2,000  feet;  the  value  of  T  is  20  seconds.  Putting  these 
values  in  the  equation,  it  becomes 

2,000  =  20  x  V.     Hence  V  =  100. 

26.  The  motion  of  a  body  produced  by  the  action  of  a 
constant  force  alone,  will  be  uniformly  accelerated.  The 
difficulties  in  the  way  of  any  accurate  experiment  upon  uni- 
formly accelerated  motion  are  overcome  by  At  wood's  ma- 
chine. (G.  27,  77,  78  ;  A.  132-135.) 

A  constant  Force.  —  Bj*  a  constant  force  we  mean  a 
force  which  acts  upon  a  moving  body  all  the  time  alike.  The 
force  of  gravitation  is  the  most  perfect  example  of  a  constant 
force. 

Uniformly  accelerated  Motion.  —  The  motion  of  a 
body  is  uniformly  accelerated,  when  its  velocity  increases 
equally  in  successive  units  of  time ,  as,  for  example,  five 
feet  the  first  second,  eight  feet  the  next  second,  eleven  feet 
the  third  second,  fourteen  feet  the  fourth,  and  so  on. 

The  motion  of  a  falling  body  is  the  most  perfect  example 
known  of  uniformly  accelerated  motion.  It  would  be  a 
perfect  example,  were  it  not  for  the  resistance  of  the  air. 

Difficulties  in  the  way  of  Experiment.  —  But  there 
are  three  difficulties  in  the  way  of  accurate  experiments  upon 
the  motion  of  a  body  falling.  1st,  This  motion  is  so  rapid 
that  no  accurate  observations  can  be  made.  2d,  It  is  sub- 
ject to  the  resistance  of  air,  which  reduces  its  velocity.  3d, 
The  friction  of  an}T  apparatus  used  is  likely  to  impede  it. 

These  Difficulties  overcome  by  Atwood's  Machine. 
—  These  difficulties  are,  for  the  most  part,  overcome  by 
Atwood's  machine  (Fig.  37).  .  Two  heavy  weights,  A  and 
B,  are  fastened  to  the  ends  of  a  small  cord  which  passes 
over  a  grooved  wheel,  D.  Each  end  of  the  axis  of  this  wheel 
rests  on  the  circumferences  of  two  other  wheels.  This  set 


72 


NATURAL  PHILOSOPHY. 


Fig.  37. 


of  wheels  may  be  supported  by  a 
bracket  firmly  fixed  to  the  wall  of 
a  room,  several  feet  above  .the  floor. 
The  standard  C  L,  reaching  to  the 
floor,  is  graduated  ;  upon  it  is  a 
movable  ring,  which  allows  the 
weight  A  to  pass  through  it ;  and 
a  table  below,  which  arrests  the 
motion  of  the  weight  at  any  desired 
point.  The  time  of  motion  is  meas- 
ured by  the  pendulum  F. 

The  two  weights  A  and  B  are 
made  exactly  equal,  and  of  course, 
when  left  to  themselves,  will  re- 
main at  rest.  But,  if  a  small  bar 
of  brass  be  laid  upon  the  weight  A, 
motion  takes  place,  due  entirely  to 
the  action  of  gravitation  upon  the 
bar. 

Now,  suppose  the  large  weights 
each  to  be  31^  ounces,  and  the 
weight  of  the  small  bar  to  be  one 
ounce.  When  they  all  move,  64 
ounces  are  in  motion,  but  this  mo- 
tion is  caused  by  the  force  which 
acts  upon  the  one-ounce  bar.  It 
is  evident,  that,  if  the  force  is  the 
same,  64  ounces  will  move  only  -^ 
as  fast  as  one  ounce.  The  motion 
of  the  weights  is  produced  by  a 
constant  force,  gravitation ;  but  it 
is  only  -fa  as  rapid  as  when  the 
bodies  fall  freely.  A  sloiu  motion 
is  thus  obtained.  The  resistance 
of  the  air  against  the  small  sur- 
faces of  the  ends  of  the  heavy 


NATURAL   PHILOSOPHY.  16 

weights  is  very  slight  when  they  move  slowly.  The  friction 
of  the  wheels  at  the  top  is  trifling.  And  thus  the  three  diffi- 
culties in  the  way  of  experiment  are  overcome. 

27.  By  experiments  with  At  wood's  machine  we  may 
prove  :  — 

1st,  That  a  body  moving  under  the  influence  of  gravita- 
tion during  any  interval  of  time  will  gain  a  velocity  which, 
acting  alone,  will  carry  the  body  twice  as  far  in*  the  next 
equal  interval. 

2d,  That  gravitation  will  add  to  the  motion  of  a  body  just 
as  much  in  every  interval  of  time  as  it  produced  in  the  first. 

By  the  help  of  these  principles  we  may  analyze  the  motion 
of  a  falling  body.  From  the  diagram  which  represents  this 
analysis,  we  may  construct  a  table  which  shall  contain  the 
values  of  Time,  Space,  and  Velocity ;  and  from  this  table 
obtain  the  Laws  which  govern  the  motion,  and  the  Formulas 
by  which  problems  may  be  solved. 

Proof  of  the  first  Principle,  —  Let  the  weight  A,  carry- 
ing the  small  bar,  be  brought  to  the  top  of  the  gradu- 
ated standard,  and  let  the  ring  C  be  placed  three  inches 
below.  Suppose  that,  in  one  second  after  its  release,  A  falls 
to  the  ring.  The  small  bar  will  be  caught  off  by  the  ring  ; 
the  weight  A  will  pass  through,  and  in  the  next  second  it  will 
be  found  to  go  exactly  six  inches.  By  putting  the  ring  at 
different  places  on  the  standard,  it  will  be  found  that  in  every 
case,  as  in  the  one  just  described,  the  body  moving  under  the 
influence  of  gravitation  during  any  interval  of  time  will  gain 
a  velocity  tvhich,  alone,  will  carry  the  body  twice  as  far  in 
the  next  equal  interval. 

Proof  of  the  second.  Principle.  —  If  the  weight  and  bar 
fall  three  inches  in  one  second,  they  will  be.  found  by  experi- 
ment to  fall  twelve  inches  in  two  seconds.  Hence  the  dis- 
tance fallen  in  the  second  interval  is  nine  inches.  If  the  bar 
were  taken  off  at  the  end  of  the  first  second,  we  know  that 
the  weight  would  go  alone  six  inches  in  the  next.  It  is  clear, 


74  NATURAL   PHILOSOPHY. 

then,  that  the  bar  acting  in  the  last  second  adds  a  motion 
of  three  inches,  the  same  amount  as  it  produced  in  the  first. 
Repeated  experiments  show  that  gravitation  will  add  to  the 
motion  of  a  falling  body  just  as  much  in  each  second  as  it 
produced  in  the  first. 

Analysis  of  the  Motion  of  a  falling-  Kody. — Now  sup- 
pose a  body  to  fall  from  the  point  A  (Fig.  38), 
toward  the  point  D.  In  the  first  second  it  will  fall 
a  certain  distance,  which  we  will  represent  by  A  B. 
For  a  moment  suppose  the  force  of  gravity  should 
cease  to  act :  the  bod}*  would  still  move  on,  and  we 
know  (b}T  the  first  principle)  that  it  would  go  in 
the  next  second  just  twice  as  far  as  it  did  in  the 
first.  Then  mark  below  B  two  spaces,  each  equal 
to  A  B,  to  represent  this  distance,  and  mark  it  with 
a  heavy  line,  that  the  eye  ma}T  see  at  a  glance  that 
it  is  the  distance  due  to  velocnyy  alone.  But  we 
know  (b}T  the  second  principle)  that  gravitation  in 
this  second  will  add  a  space  just  equal  to  A  B. 
Marking  this  additional  space  in  the  figure,  we  find 
that  in  two  seconds  the  bod}'  will  fall  to  C. 

In  two  seconds  the  body  has  fallen  four  spaces  :  in 
the  next  two  seconds  it  will  go  twice  as  far,  eight 
spaces,  by  velocity  alone.  In  the  first  of  these  two 
seconds,  which  is  the  third  second  of  its  fall,  the 
body  will  go  one  half  that  distance,  or  four  spaces, 
by  velocity.  The  force  of  gravity  adds  another 
space,  so  that  at  the  end  of  three  seconds  the  body 
will  be  found  at  D. 

To  find  the  distance  passed  in  the  fourth  second, 
notice  .that  in  the  first  three  seconds  it  has  passed 
D  •"•j1""    nine  spaces  ;  that  in  the  next  three  seconds  it  will 
go,  by  its  velocity  alone,  eighteen  spaces,  and  that 
lg'      '  in  one  of  these  three  seconds,  which  would  be  the 
fourth  second,  it  would  go  six  spaces.     Mark  six  spaces  for 
velocity,  and  add  one  for  the  action  of  gravitation. 


T. 


Id 
3d 


NATURAL  PHILOSOPHY.  75 

Construction  of  the  Table. —  Now,  in  this  diagram  the 
values  of  time,  space,  and  velocity,  stand  clearly  before 
us,  and  we  may  put  them  into  a  tabular  form.  In  the  first 
column,  headed  T,  put  the  number  of  seconds,  1,  2,  3,  4.  In 
the  second  column,  headed  S,  put  the 
total  space  passed  over  at  the  end  of 
these  seconds,  representing  the  distance 
A  B  by  d.  In  the  third  column,  headed 
V,  put  the  velocities  gained  at  the  end 
of  each  of  the  seconds.  And,  finally,  in 
the  fourth  column,  headed  s,  put  the 
spaces  passed  in  each  separate  second. 

From  the  Table  obtain  the  Laws.  —  The  relation  be- 
tween time,  space,  and  velocity,  may  be  seen  by  comparing 
their  values  given  in  this  table. 

Notice,  FIRST,  that  the  values  of  S  have  the  same  ratio  as 
the  squares  of  the  value  of  T.  For  instance,  take  the  spaces 
4c£  and  9cZ,  with  the  corresponding  times  2  and  3,  we  find 
that  4  d  :  9  d  : :  2'2  :  32.  Hence  the  spaces  passed  by  a  falling 
body  in  different  times  are  as  the  squares  of  the  times. 

Notice,  SECOND,  that  the  values  of  V  have  the  same  ratio 
as  the  values  of  T.  Thus  we  find  that  the  velocities  4d  and 
6d  have  the  same  ratio  as  2  and  3,  the  corresponding  values 
of  time.  Hence  the  velocities  of  a  falling  body  at  the  end 
of  successive  intervals  of  time  ivill  vary  as  the  time  of  fall. 

Notice,  THIRD,  that  the  spaces  passed  in  separate  seconds 
(the  values  of  s)  are  as  the  odd  numbers,  1,  3,  5,  7,  &c. 

From  the  Table  also  obtain  Formulas.  —  It  will  be 
seen,  that  by  squaring  any  one  of  the  values  of  T  in  the 
table,  and  then  multiplying  by  d,  the  corresponding  value  of 
S  will  be  obtained.  Hence, 

S-T2d.     (1.) 

Again,  we  may  discover  that  if  the  value  of  T  in  any  case 
be  multiplied  by  2  d,  the  corresponding  value  of  V  will  be 
produced.  Hence, 

V  =  2dT.     (2.) 


76  NATURAL   PHILOSOPHY. 

We  see,  again,  that  if  the  value  of  S  in  any  case  be  mul- 
tiplied by  cZ,  the  square  root  of  this  product,  multiplied  by  2, 
gives  the  value  of  V.  Hence, 

V=2VS^.     (3.) 

Finally,  a  little  attention  will  show,  that  if  the  value  of  T 
in  an}^  case  be  multiplied  by  2,  the  product  diminished  by  1, 
and  the  remainder  multiplied  by  d,  the  corresponding  value 
of  s  will  be  obtained.  Hence, 

s=  (2  T-  1)  d.     (4.) 

Acceleration.  —  The  velocity  added  in  each  interval  of 
time  is  called  the  ACCELERATION.  The  acceleration  is  always 
represented  by  the  letter  g.  The  diagram  shows  that  d  = 

\g- 

Let  us  put  ^  g,  which  is  the  value  of  cZ,  in  place  of  c?,  and 
the  four  formulas  become, 

S=i?T2.  (1.) 

V  =  gT^_  (2.) 

V  =  V*S0.  (3.) 

s=Jgr(2T-l).  (4.) 

The  Value  of  </.  —  In  all  cases  g  represents  twice  the  dis- 
tance passed  by  the  body  in  the  first  interval  of  time.  Its 
value  will  be  different  for  different  forces.  When  gravitation 
is  the  constant  force  which  causes  the  motion,  the  value  of 
g  is  32£  feet. 

By  these  Formulas  solve  Problems.  —  By  the  use 
of  these  four  formulas,  all  problems  in  uniformly  accelerated 
motion  may  be  solved.  A  single  illustration  will  show  how 
they  may  be  used.  If  a  stone  be  dropped  into  a  well  whose 
mouth  is  144J  feet  above  the  water,  how  long  will  it  take  to 
reach  the  water?  Since  gravitation  produces  this  motion, 
the  value  of  g  is  32J  feet.  The  144|  feet  is  the  value  of  S, 
and  the  value  of  T  is  required.  The  relation  between  these 
elements  is  expressed  b}'  the  formula  S  =  -J  g  T2 ;  and  by  sub- 
stituting the  given  values  we  have  144|  =  T2  X  16^.  The 
value  of  T,  from  this  equation,  is  3  seconds. 


NATURAL   PHILOSOPHY.  77 

SECTION   II. 
MOTION  PRODUCED  BY  MORE  THAN  ONE  FORCE. 

28.  If  a  body  be  acted  upon  by  two  forces  which,  sepa 
ratety,  would  cause  it  to  describe  the  adjacent  sides  of  a 
parallelogram,  they  will  be  equivalent  to  a  single  force,  caus- 
ing it  to  move  through  the  diagonal  of  the  parallelogram. 

Hence  the  effect  of  two  forces  may  be  found  by  represent- 
ing them  by  the  two  sides  of  a  parallelogram,  and  then 
drawing  the  diagonal.  (A.  111-117.) 

If  a  Body  l>e  acted  on  by  two  Forces.  —  Forces  sel- 
dom act  singly.  It  is  b}'  the  combined  action  of  at  least  two, 
often  of  more,  that  almost  every  motion  is  produced.  The 
action  of  two  forces  may  be  illustrated  by  a  very  simple  experi- 
ment. Place  a  ball  at  one  corner  of  the  table.  Snap  it  with 
the  fingers,  lengthwise  of  the  table,  and  it  will  roll  along  the 
side ;  or  snap  it  across  the  table,  and  it  will  roll  across  the 
end.  But  skillfully  snap  it  both  wa}Ts  at  the  same  time,  using 
both  hands  for  the  purpose,  and  it  will  roll  in  neither  of  these 
directions,  but  will  move  obliquely  across  the  table. 

The  same  thing  is  true  of  the  action  of  natural  forces, 
such  as  wind  and  tide.  A  ship,  driven  north  by  a  direct 
wind,  ma}*  at  the  same  time  be  drifted  east  by  a  tide  moving 
eastward.  If  so,  it  will  at  every  mo-  s  c 

ment  be  moving  north  and  east,  or  in 
a  straight  line  toward  the  north-cast. 

Acting  along-  the  adjacent  Sides 
of  a  Parallelogram.  —  The  condi- 
tions of  the  motion  of  both  the  ball 
and  the  ship  may  be  represented  to  the  Fig'  39* 

eye.  Let  A  (Fig.  39)  represent  the  original  place  of  the 
ship.  Suppose  that  while  the  wind,  if  acting  alone,  would 
move  the  ship  to  B,  the  force  of  the  stream,  if  acting  alone, 


78  NATURAL  PHILOSOPHY. 

would  move  it  to  D  in  the  same  time:  then,  when  both  act 
at  once,  the  body  will  neither  go  to  B  nor  D,  but  will  go 
along  the  diagonal  line  A  C,  and  will  reach  the  point  C  in 
the  same  time  it  would  have  taken  to  go  to  either  B  or  D. 

They  are  equivalent  to  a  single  Force.  —  The  two 
forces,  acting  in  the  directions  A  B  and  A  D,  produce  a  sin- 
gle motion  along  the  line  AC.  A  single  force  acting  in  the 
direction  of  A  C  would  have  produced  the  same  effect. 
Hence  two  forces,  acting  in  the  directions  of  the  sides  of  the 
parallelogram,  are  equivalent  to  a  single  force  acting  in  the 
direction  of  the  diagonal. 

The  separate  forces  are  called  COMPONENTS  ;  the  single  force 
which  would  produce  the  same  effect  is  called  the  RESULTANT  ; 
and  the  process  of  finding  the  resultant  is  called  the  COMPO- 
SITION OF  FORCES. 

The  Resultant  of  two  Forces  may  be  found.  —  The 
resultant  of  two  forces  ma}'  be  found  by  representing  them  by 
two  adjacent  sides  of  a  parallelogram,  and  then  drawing  the 
diagonal.  The  lengths  of  the  lines  rep- 
resent the  strength,  or  the  intensity,  of 
the  forces. 

In  the  case  of  the  ship,  for  instance, 
suppose  the  wind  able  to  drive  it  ten 
miles,  while  the  tide  can  drift  it  five 
miles.  To  find  the  actual  path  of  the 
ship,  draw  the  line  A  B  (Fig.  40),  to 
represent  the  ten  miles,  and  then  the 
line  A  D,  at  right  angles  to  it,  and  one- 
half  as  long,  to  represent  the  five  miles. 


Fig.  40.  Draw  the  lines  B  C  and  C  D,  to  complete 

the  parallelogram,  and  then  draw  the  diagonal  A  C.  This  line 
represents  the  path  of  the  ship,  or  the  resultant  of  the  two 
forces. 

The  Resultant  of  more  than  two  Forces.  —  If  more 
than  two  forces  act  at  once,  the  resultant  of  all  may  be 
found  by  repeating  the  process.  Find  the  resultant  of  two 


NATURAL  PHILOSOPHY.  79 

of  them  first ;  then  compare  this  resultant  and  a  third  force  ; 
this  second  resultant  and  a  fourth  force  ;  and  so  continue 
until  all  the  forces  have  been  used  :  the  last  resultant  will  be 
the  resultant  of  all  the  forces. 

29.  Any  force  may  be  resolved  into  two  others,  which, 
acting  together,  would  produce  the  same  effect.  This  is  done 
when  we  wish  to  know  what  part  of  a  given  force  can  be  made 
available  in  a  direction  different  from  that  in  which  it  acts. 

A  Force  may  be  resolved.  —  To  find  the  components 
of  a  given  force,  we  ma}*  represent  it  by  a  line,  and  make 
this  line  the  diagonal  of  a  parallelogram ;  the  adjacent  sides 
of  this  parallelogram  will  represent  the  components.  More 
than  one  parallelogram  can  be  drawn  on  the  same  diagonal ; 
so  more  than  one  set  of  components  may  be  found  for  a 
single  force. 

The  process  of  finding  the  components  of  a  single  force 
is  called  the  RESOLUTION  OF  FORCES. 

To  find  the  Component  which  acts  in  a  given  Direc- 
tion.—  When  a  ball  is  thrown  obliquely  against  the  floor, 
it  acts  upon  it  with  less  force  than  when  thrown  perpen- 
dicularly against  it.  But  a  part  of  the  force  will  still  be 
exerted  perpendicularly  against  the  floor. 

To  illustrate  this  important  point,  let  a  ball,  A  (Fig.  41), 
be  thrown  against  the 
floor,  striking  it  at  C. 
We  may  let  the  line 
A  C  represent  the  force 
with  which  the  ball  is 
thrown.  Now  construct 
the  parallelogram,  by 
drawing  the  lines  A  B 
and  C  D  perpendicular  Fig'  41' 

to  the  floor,  and  then  A  D  parallel  to  it.  The  lines  A  B  and 
A  D  represent  the  components  of  the  force  A  C. 

The  line  A  B  represents  the  amount  of  force  exerted  per' 


80  NATURAL   PHILOSOPHY. 

pendicularly  against  the  floor.  To  make  the  illustration 
more  specific,  we  will  suppose  that,  measuring  the  lines  A  C 
and  A  B,  we  find  the  latter  to  be  f  as  long  as  the  former ;  if 
so,  then  the  force  exerted  perpendicular  to  the  floor  will  be  f 
of  the  force  with  which  the  ball  is  thrown. 

To  find  the  component  which  acts  in  any  given  direction, 
we  ma}'  represent  the  original  force  by  a  straight  line,  and 
make  it  the  diagonal  of  a  parallelogram,  one  of  whose  adja- 
cent sides  is  in  the  direction  given.  This  side  will  represent 
the  force  required. 

30.  Two  forces  may  act  upon  different  points  of  a  body  in 
the  same  direction  :  their  resultant  will  be  equal  to  their  sum. 

The  point  of  the  bod}'  to  which  this  resultant  is  applied 
will  be  as  many  times  nearer  to  the  greater  force  than  the 
smaller  one,  as  the  greater  exceeds  the  smaller  in  intensity. 

The  weight  of  a  bod}'  is  only  the  resultant  of  a  set  of  par- 
allel forces  acting  upon  it  in  the  same  direction  ;  and  what  is 
called  the  center  of  gravity  is  the  point  of  application  of  this 
resultant.  (G.  69  ;  A.  202,  207,  210.) 

Two  Forces  in  the  same  Direction.  —  When  two  forces 
act  upon  a  body  in  the  same  direction,  they  produce  the 
same  effect  as  a  single  force  equal  to  their  sum.  If  two 
horses,  for  example,  draw  a  carriage,  one  with  a  force  of 
two  hundred  pounds,  and  the  other  with  a  force  of  three 
4  D  JK  hundred  pounds,  it  is  clear  that 

a  single  horse  exerting  a  force 
of  five  hundred  pounds  would 
produce  the  same  effect. 

The  Point  of  Application. 
— But  if   a    single   force   is   to 
take   the   place    of  two   others, 
and   produce    exactly   the   same 
Flg*  42'  motion  as  they  would  when  act- 

Ing  together,  at  what  point  of  the  body  shall  it  be  applied  ? 
Suppose  the  body  represented  by  A  B  (Fig.  42),  to  be 


NATURAL  PHILOSOPHY.  81 

acted  upon  by  two  forces,  represented  by  the  lines  c  and  d, 
one  just  half  the  length  of  the  other,  the  lesser  force  being 
twenty-five  pounds,  the  greater  fifty  pounds.  Then  the  line 
r,  just  as  long  as  both  together,  will  represent  the  resultant, 
a  force  of  seventy-five  pounds.  Now,  if  this  resultant  is  to 
move  A  B  exactly  as  the  two  components  would,  it  must  be 
applied  at  some  point,  D,  as  many  times  farther  from  A  than 
from  B  as  the  force  at  A  is  times  less  than  that  at  B.  Since 
c  is  just  half  of  d,  the  distance  A  D  must  be  just  twice  as 
great  as  B  D. 

The  Weight  of  a  Body.  —  A  body  falling  freely  is  an 
example  of  motion  caused  by  the  action  of  parallel  compo- 


Fig.  43. 

nents.  For,  since  the  force  of  gravitation  acts  upon  every 
molecule  of  the  bod}T,  we  may  regard  the  entire  force  as  made 
up  of  as  many  separate  forces  as  there  are  molecules'.  The 
sum  of  all  these  components  is  their  resultant,  and  the  value 
of  this  resultant  is  the  weight  of  the  bod}\ 

The  Center  of  Gravity. — The  point  of  application  of 
this  resultant  is  the  center  of  gravity.  The  center  of  grav- 
ity is  usually  defined  to  be  that  point  in  a  body,  which  being 
supported,  the  body  will  rest  in  any  position.  One  can  bal- 
ance a  book  on  the  tip  of  his  finger :  the  tip  of  the  finger 
must  be  exactly  under  the  center  of  gravity  of  the  book. 
This  point  being  supported,  the  whole  body  will  rest. 

The  center  of  gravity  is  the  exact  middle  point  of  a  body 


82  NATURAL   PHILOSOPHY. 

of  uniform  density ;  it  is  toward  the  heavier  side  of  one  that 
is  not. 

In  Fig.  43  the  center  of  gravity  in  each  bod}-  is  at  G. 

What  is  the  Line  of  Direction  ?  —  Now  imagine  a  ver- 
tical line  drawn  through  the  center  of  gravity* ,  as  shown  by 
the  vertical  dotted  lines  in  Fig.  43.  This  line  will  show  the 
direction  in  which  the  body  would  fall  if  it  were  left  without 
support ;  and  it  is  called  the  line  of  direction. 

Principle  of  Stability That  a  body  may  stand  upon 

a  plane  surface  without  falling,  the  line  of  direction  must 
pass  through  its  base. 


Fig.  44. 

One  body  stands  more  firmly  than  another,  only  because  it 
is  more  difficult  to  throw  its  line  of  direction  beyond  its 
base.  A  load  of  hay  is  easily  overturned,  because,  the  cen- 
ter of  gravity  being  high,  the  line  of  direction  may  be  easily 
thrown  outside  the  base.  A  load  of  stone,  having  no  greater 
weight,  stands  firm,  because,  the  center  of  gravity  being  low, 
the  line  of  direction  can  with  difficulty  be  thrown  beyond  its 
base. 

Carriages  may  lean  considerably  to  one  side  without  over- 
turning (Fig.  44)  ;  but  an  accident  is  sure  to  happen  if  they 
lean  so  far  as  to  throw  the  line  of  direction  beyond  the  lower 
side  of  the  wheel. 


NATURAL   PHILOSOPHY.  83 

Animals  instinctively  incline  their  bodies  always  in  such  a 
way  as  to  keep  their  center  of  gravit}*  over  the  space  between 
their  feet. 

The  showman  offers  a  gold  coin  to  the  boy  who  will  stand 
with  his  heels  pressed  against  the  wall  of  a  room,  and  then 
pick  it  from  the  floor  in  front  of  him  without  falling.  He  is 
perfectly  safe  in  making  the  offer.  For  no  one  can  stoop 
without  falling,  unless,  when  he  throws  his  head  forward,  he 
can,  at  the  same  time,  throw  some  other  part  of  his  body 
backward  far  enough  to  keep  his  center  of  gravity  over  his 
feet.  He  can  not  do  this  with  his  heels  pressed  against  a 
wall,  and  therefore  can  not  win  the  coin. 

31.  Curved  motion  is  produced  by  the  action  of  at  least 
two  forces,  one  of  which  is  a  constant  force,  the  other  may 
not  be. 

The  motion  of  a  projectile  is  caused  by  the  constant  force 
of  gravitation,  and  the  impulse  by  which  it  is  thrown.  (Gr. 
53;  A.  159,  1G4.) 

Curved  Motion.  —  Whoever  watches  the  varied  and 
beautiful  motions  in  nature,  will  find  that  they  all  take  place 
in  curves.  In  the  ripples  of  the  lake  and  the  billows  of  the 
sea,  he  wall  see  a  wonderful  variety  of  curved  motions.  The 
winds,  and  the  clouds  they  cany,  move  in  curves.  Every 
swaying  branch  and  leaf,  and  every  nodding  stalk  of  grass, 
moves  in  a  curve. 

Is  produced  by  at  least  Two  For- 
ces. —  The  motion  of  a  ball  when  fast- 
ened to  the  end  of  a  string,  and  whirled 
around  the  hand,  is  an  example  of 
curved  motion.  It  is  produced  by 
the  action  of  two  forces.  The  impulse 
of  the  hand  H  (Fig.  45),  which  starts 
the  ball,  would,  if  it  could  act  alone, 
carry  it  in  a  straight  line  from  A  toward  E.  But  the 
string  H  A,  held  firmly  by  the  hand,  is  a  constant  force 


£4  NATURAL  PHILOSOPHY. 

which  pulls  it  away  from  that  path.  The  resultant  of  these 
two  forces  is  represented  by  the  circumference  A  B  C  D. 

One  of  which  is  Constant.  —  In  the  example  just 
given,  the  force  of  the  hand  is  an  impulsive  force  ;  that  of 
the  string,  a  constant  force  ;  and  a  curved  motion  is  the  result. 
Two  impulsive  forces  will  cause  motion  in  a  straight  line ; 
two  equal  constant  forces  will  do  the  same.  Two  constant 
forces  that  are  unequal  will  cause  a  curved  motion  ;  one,  at 
least,  of  the  forces  must  be  constant. 

Tlic  Central  Forces.  —  These  two  forces  by  which  curved 
motion  is  produced  are  called  the  CENTRAL  FORCES.  One  of 
them  always  acts  toward  the  center  of  the  circle  around 
which  the  bod}'  is  moving,  and  the  other  always  in  the  direc- 
tion of  a  tangent.  The  force  which  acts  toward  the  center 
of  the  circle  around  which  the  body  moves  is  called  the 
CENTRIPETAL  FORCE.  The  force  of  the  string  which  holds 
the  ball  in  its  circuit  is  the  centripetal  force. 

Let  the  centripetal  force  be  destroyed,  and  the  other  cen- 
tral force  will  cause  the  ball  to  fry  in  a  straight  line,  as  B  F 
or  C  K. 

The  most  wonderful  examples  of  the  action  of  central  forces 
are  seen  in  the  majestic  movements  of  the  heavenly  bodies. 
Their  orbits  are  ellipses.  The  impulse  which  drives  the 
planets  forward,  and  the  attraction  of  the  sun,  are  the  cen- 
tral forces  which  hold  them  in  their  oroits. 

Centrifugal  Force.  —  The  ball,  when  moving  in  the  cir- 
cle, is  trying  all  the  time  to  move  in  a  straight  line  instead. 
This  is  the  effect  of  its  inertia.  The  string  must  overcome 
this  inertia  at  every  point,  and  this  resistance  of  the  ball  is 
a  pull  lengthwise  of  the  string  outward.  This  resistance  to 
deflection  from  a  straight  line  is  called  the  CENTRIFUGAL 
FORCE.  This  force  takes  no  part  in  the  production  of  the 
curved  motion.  It  is  simply  the  re-action  of  the  moving  bod}' 
against  the  centripetal  force. 

Experiment.  —  A  simple  and  pleasant  experiment  may  be 
performed  to  illustrate  the  effect  of  centrifugal  force.  To 


NATURAL   PHILOSOPHY.  85 

the  handle  of  a  small  pail,  filled  with  water,  tie  a  cord  firmly. 
Grasp  the  cord,  and  swing  the  pail,  fearlessly,  in  a  vertical 
circle  over  the  head  ;  the  centrifugal  force  will  overcome  the 
force  of  gravity,  so  that  not  a  drop  of  water  will  fall,  even 
when  the  pail  is  bottom  side  up  over  the  head. 

Illustration*.  —  Circus-riders  incline  their  bodies  toward 
the  center  of  the  ring  around  which  the}"  ride,  that  the  cen- 
trifugal force  may  not  throw  them  from  their  horses.  Car- 
riages, in  very  rapid  motion  around  the  corner  of  a  street, 
are  in  danger  of  being  overturned  by  this  force. 

Projectiles Any  body  thrown  into  the  air  is  a  pro- 
jectile. The  stone  from  the  hand,  the  ball  from  the  gun,  and 
the  arrow  from  the  bow,  are  familiar  examples  of  projectiles. 

Their  Motion  is  due  to  two  Forces.  —  Leaving  resist- 
ance of  the  air  out  of  account,  the  motion  of  a  projectile  is 
due  to  the  action  of, 

1st,  The  impulse  which  starts  it  on  its  journey  ;  and, 

2d,  the  constant  force  of  gravity. 

Range.  —  The  horizontal  distance  is  called  the  RANGE  <y 
the  RANDOM  of  the  projectile. 

The  range  of  a  ball  thrown  from  my  hand  is  measured 
from  my  feet  along  the  level  ground  to  the  spot  where  the 
ball  strikes. 

This  distance  depends  upon  the  force  applied  to  the  pro- 
jectile, and  the  angle  at  which  it  is  thrown.  Theory  requires 
that  the  random  be  greatest  when  the  projectile  is  thrown  at 
an  angle  of  45° ;  but  the  resistance  of  the  air  veiy  much 
modifies  the  motion,  so  that,  in  practice,  the  greatest  range 
is  obtained  at  an  angle  much  below  45°.  The  greatest  range 
of  an  arrow  is  when  the  angle  is  about  36°. 

The  science  of  gunnery  rests  upon  the  laws  of  projectiles. 
The  most  skillful  gunner  is  he  who  can  most  accurate!}', 
under  all  circumstances,  compare  and  combine  the  forces  of 
gunpowder,  gravitation,  and  the  resistance  of  the  air. 


86 


NATURAL  PHILOSOPHY. 


SECTION  III. 

ON  THE  MOTION  OF  LIQUIDS. 

32.  Water  will  issue  from  an  opening  in  the  side  of  a 
vessel  with  the  same  velocit}'  which  a  body  would  gain  by 
falling  from  the  surface  of  the  water  to  the  center  of  the 
opening. 

Hence  the  velocit}r  of  the  jet  of  water  will  depend  only 
on  the  distance  of  the  orifice  below  the  surface  of  the 
water  in  the  vessel,  and  may  be  calculated  by  the  formula, 
V  = 


(A.  34G,  353-355.) 

The  Velocity  of  a  Jet  of  Water  the  same  as  that 
of  a  Falling-  Body.  —  To  prove  this  principle,  we  must 
remember  :  first,  that  water,  confined  in  pipes,  will  rise  as 
high  as  the  source  from  which  it  comes  ;  second,  that  a 
body  thrown  upward  starts  with  the  same  velocity  that  it 
has  when  it  gets  back. 

In  Fig.  46,  a  bent  tube,  A,  extends  from  near  the  bottom 

of  a  vessel  of  water.  The 
water  rises  as  high  in  the  tube 
as  in  the  vessel  ;  it  is  the  up- 
ward pressure  of  the  water  at 
A  that  pushes  it  up.  The 
same  force  would  be  exerted 
on.  the  water  at  A,  if  the  tube 
were  cut  off  at  that  point, 
and  it  would,  if  not  resisted, 
throw  the  water  to  the  same 
height,  as  shown  on  the  other 
side  of  the  figure,  at  B.  But  the  velocity  with  which  it 
must  start  from  B,  to  reach  the  level  of  R,  is  the  same  it 
would  gain  by  falling  from  that  level  back  to  B.  If  the 
tube  were  cut  off  at  C,  the  water  would  issue  under  the  same 


Fig.  46. 


NATURAL  PHILOSOPHY.  87 

pressure,  and,  therefore,  with  the  same  velocity.  Hence  the 
velocity  with  which  the  water  issues  is  the  same  as  that  of 
a  body  falling  from  the  surface  of  the  water  down  to  the 
center  of  the  orifice. 

The  Velocity  of  the  Jet  depends  011  the  Distance  of 
the  Orifice  below  the  Level  of  the  Water.  —  The  velo- 
city of  a  falling  body  depends  only  on  the  height  from  which  it 
has  fallen.  All  bodies,  whatever  be  their  size  or  nature,  fall 
with  equal  velocities.  In  the  same  manner,  all  liquids,  how- 
ever different  in  nature,  will  issue  with  equal  velocities,  if 
the  openings  from  which  they  are  thrown  are  at  the  same  dis- 
tance from  the  surface  of  the  liquid  in  the  reservoir. 

Velocity  calculated  by  the  Formula,  V  =  \/2Sg.  — 
Now,  the  velocity  of  a  falling  body  is  given  by  the  equation 


V  =  \/2  S  g,  and  it  is  clear  that  the  velocity  of  a  jet  of  water 
will  be  given  by  the  same  formula,  if  S  represents  the  dis- 
tance of  the  orifice  below  the  level  of  the  water  in  the  vessel. 
If,  for  example,  we  would  know  the  velocity  of  a  jet  of 
water  from  an  orifice  thirt}T-six  feet  below  the  surface  in  .a 
reservoir,  we  put  36  for  S  in  the  formula.  It  then  reads  : 
V  =  \/2  x  36  x  02!.  The  value  of  V  is  48  ;'  then  the  velo- 
city of  the  water  is  48  feet  a  second. 

33.  The  quantity  of  water  discharged  from  an  orifice, 
depends  upon  its  velocity,  the  size  of  the  orifice,  and  the 
time  of  flow.  It  may  be  found  by  multiplying  the  values  of 
these  three  things  together. 

To  calculate  the  Quantity.  —  For  example,  how  much 
water  will  flow  from  an  orifice  of  1J  square  feet  area,  at  a 
depth  of  9  feet  below  the  surface  of  the  water,  in  10  seconds  ? 

At  a  depth  of  9  feet  the  water  will  issue  with  a  velocity, 
v  =  \/2  X  9  x  32  =  24  ft.  Now,  if  the  opening  were  one 
square  foot,  then  24  cubic  feet  would  issue  in  one  second, 
and  24  x  1^  X  10  =  360  cubic  feet  must  issue  from  the  ori- 
fice of  1J  square  feet,  in  10  seconds. 


88  NATURAL  PHILOSOPHY. 

The  rule  is  concisely  expressed  by  the  formula  :  — 

q  =  v  x  a  x  t,  in  which 

q  represents  the  quantity  of  water  discharged, 
v  represents  the  velocity, 
a  represents  the  area  of  the  orifice, 
t  represents  the  time  of  flow. 

In  this  equation  there  are  four  things,  and  it  is  clear  that, 
any  three  of  them  being  given,  the  fourth,  whichever  it  may 
be,  can  be  found.  A  single  illustration  will  show  how  this  is 
done. 

Suppose  10,000  cubic  feet  of  water  must  be  discharged  in 
60  seconds,  from  an  orifice  so  far  below  the  surface  of  the 
water  that  the  velocity  of  the  jet  is  250  feet  a  second  :  how 
large  must  the  orifice  be  made? 

In  this  problem,  the  value  of  v  is  given,  250  feet ;  the 
value  of  t  is  60  seconds ;  the  value  of  q  is  10,000  cubic  feet ; 
the  value  of  a  is  wanted.  By  putting  the  given  values  into 
the  equation  it  becomes  :  — 

10,000  =  250  x  a  x  60  :  hence, 

a  —  |  of  a  square  foot,  or  96  square  inches. 

34.  The  velocity  of  a  jet  of  water,  and  the  quantity  dis- 
charged, are  found  in  practice  to  be  much  less  than  the 
foregoing  theory  would  give.  The  actual  amount  may  be 
increased  by  using  short  tubes  of  different  shapes.  (G.  210- 
213.) 

The  Quantity  in  Practice  less  than  in  Theory.  —  If 

we  examine  a  jet  of  water  flowing  from  an  orifice  in  the  side 
of  a  thin  vessel,  we  shall  see  that  it  grows  rapidly  smaller,  so 
that,  at  a  little  distance,  its  size  is  only  about  two-thirds  as 
great  as  at  the  orifice.  Beyond  this  point  the  contraction  of 
the  jet  is  gradual.  The  rapid  contraction  near  the  orifice  is 
due  to  cross  currents,  caused  by  the  water  flowing  toward  the 
orifice  from  different  directions  in  the  vessel ;  these  currents 
may  be  seen  if  there  be  any  solid  particles  floating  in  the 
water.  If  the  jet  were  the  full  size  of  the  orifice,  the 


NATURAL  PHILOSOPHY.  89 

quantity  of  water  discharged  would  be  what  the  theory  gives  ; 
but,  since  it  is  only  about  two-thirds  as  large,  there  will  be 
only  about  two-thirds  as  much  water  discharged. 

The  Quantity  increased  by  using  Tubes.  —  Short  tubes 
inserted  in  the  orifice  are  found  to  increase  the  actual  flow. 
These  tubes  are  either  cylindrical  or  conical. 

It  is  found  that  a  cylindrical  tube,  whose  length  is  not 
more  than  four  times  its  diameter,  if  placed  in  the  orifice, 
will  increase  the  amount  discharged  to  about  .82  of  that 
which  theory  gives.  In  this  case  the  water  adheres  to  the 
sides  of  the  tube,  and  the  tube  is  kept  full,  so  that  the  con- 
traction of  the  jet  is  prevented.  Bjr  the  use  of  conical  tubes 
the  amount  discharged  may  be  made  still  greater. 

35.  A  liquid  running  freely  down  a  vertical  pipe  exerts  no 
lateral  pressure. 

A  stream  carries  the  adjacent  air  along  with  it. 

These  principles  may  be  applied  to  produce  either  a  blast 
of  air  or  a  vacuum.  (G.  193,  194  ;  A.  356.) 

No  lateral  Pressure.  —  As  the  water  falls,  its  velocity 
increases,  and  the  stream  must  be  smaller.  It  will  not  fill 
the  pipe.  The  force  of  gravit}'  is  wholly  expended  in  motion 
downward,  and  hence  there  is  no  pressure  in  any  other 
direction. 

Motion  of  the  adjacent  Air.  —  The  power  of  a  stream 
of  water  to  drag  air  along  with  it  is  often  shown  when  a 
faucet  is  opened.  If  the  stream  flows  into  a  vessel  partly 
filled  with  water,  it  penetrates  to  some  depth,  and  some- 
times, if  the  head  is  strong,  it  makes  the  water  foam  as 
if  in  violent  ebullition.  In  any  case  an  abundance  of  air- 
bubbles  may  be  seen  rising  and  breaking  at  the  surface. 
This  is  the  air  which  is  dragged  down  b}'  the  stream.  The 
adhesion  of  the  two  enables  the  stream  to  pull  the  air 
along. 

Application  to  produce  a  Blast.  —  Let  a  small  tube  (V, 
Fig.  47)  be  inserted  near  the  top  of  a  vertical  pipe.  Let 


90 


NATURAL  PHILOSOPHY. 


this  pipe  enter  a  bottle  provided  with  two  outlets,  one  near 
the  bottom  for  the  water  to  escape,  the  other  near  the  top. 

The  stream  of  water  in  C  S 
will  drag  the  air  down  the 
vertical  pipe,  causing  a  cur- 
rent to  enter  through  the 
small  tube  Y,  and  to  issue 
from  the  bottle  in  a  steady 
blast  from  the  jet  B. 

Application  to  produce 
a  Vacuum Let  the  re- 
ceiver R  be  attached  to  the 
small  tube  V,  and  the  air  in 
it  will  be  taken  out  by  the 
stream  of  water. 

Various  forms  of  appara- 
tus for  exhausting  air,  on 
this  principle,  are  construct- 
ed. In  the  Sprengel  pump, 
mercury  is  used.  The  tube 
is  rather  more  than  thirty 
inches  in  length,  and  the 
vacuum  obtained  is  almost 
perfect.  In  Bunsen's  pump, 
water  is  the  liquid,  and  the 

tube  is  about  thirty-four  feet  long  to  produce  the  best  re- 
sults. 


SECTION  IV. 

ON  THE  MOTION  OF  AIR. 

36.  Air  in  motion  is  called  wind.  Winds  are  produced  by 
the  action  of  heat  and  the  attraction  of  gravitation,  upon  the 
atmosphere ;  and,  in  case  of  the  trade-winds,  partly  by  the 
rotation  of  the  earth  on  its  axis.  (G.  927-929.) 


NATURAL   PHILOSOPHY.  91 

Wind.  —  The  motion  of  air,  called  wind,  is  due  to  a 
difference  in  the  temperature  of  two  portions  of  the  atmos- 
phere. Heat  expands  air.  One  hundred  cubic  inches  of 
hot  air  will  iveigh  less  than  a  hundred  cubic  inches  of  cold  air. 
Then,  if  a  portion  of  hot  and  light  air  is  surrounded  by  that 
which  is  colder  and  heavier,  it  will  rise,  for  the  same  reason 
that  a  cork  rises  in  water.  It  will  be  pushed  up  out  of  the 
wa}'  by  the  heavier  air,  which  takes  its  place. 

Let  us  suppose  that,  in  some  particular  part  of  the  countiy, 
the  air  becomes  heated  more  than  in  surrounding  portions. 
This  heated  and  lighter  air  will  be  pushed  up  by  air  moving 
in  from  all  directions  to  take  its  place.  This  moving  air  is 
wind.  People  residing  north  of  the  heated  place  will  observe 
a  north  wind,  and  those  south  of  it  a  south  wind. 

Now,  there  is  an  unequal  distribution  of  heat  over  the  sur- 
face of  the  earth.  It  is  caused  partly  by  the  changes  of  the 
seasons,  and  partly  by  various  local  causes.  To  it  the  pro- 
duction of  winds  is  due.  Their  direction  will  be  modified  by 
many  causes :  the  form  of  the  surface  over  which  they  pass 
is  an  important  one.  As  the  same  wind  often  blows  in  dif- 
ferent directions  on  different  sides  of  a  house,  or  as  blocks 
of  buildings  compel  the  wind  to  sweep  up  and  down  the 
various  streets  of  a  city,  so  the  hills  and  valleys  of  a  country, 
or  the  presence  of  forests  or  plains,  will  modify  the  direction 
of  the  winds  that  blow  over  them. 

The  Trade- Winds.  —  The  trade-winds  require  particular 
notice.  They  occur  in  the  equatorial  parts  of  the  earth, 
and  always  blow  in  the  same  directions.,  Over  a  surface  of 
about  30°  of  latitude  on  the  north  side  of  the  equator,  they 
blow  from  the  north-east  toward  the  south-west ;  while  south 
of  the  equator,  over  about  the  same  width  of  zone,  they 
blow  from  the  south-east  toward  the  north-west.  These  direc- 
tions are  maintained  so  constantly,  that  mariners  count  upon 
the  trade-winds  with  almost  the  same  certainty  as  upon  the 
rising  and  setting  of  the  sun. 

Due  to  Heat  and  the  notation  of  the  Earth.  —  To 


92  NATURAL   PHILOSOPHY. 

explain  this  phenomenon  we  must  remember :  first,  that  the 
equatorial  region  is  constant!}'  heated  by  the  sun  more  than 
parts  of  the  earth  either  north  or  south ;  and,  second,  that 
the  earth  revolves  from  west  to  east,  the  equatorial  parts 
moving  most  swiftly. 

The  heated  air  at  the  equator,  lighter  than  the  air  either 
north  or  south  of  it,  will  be  pushed  up,  while  currents  of 
colder  air  from  the  north  and  from  the  south  will  move 
toward  the  equator.  But  the  equatorial  parts  of  the  earth 
move  toward  the  east  more  swiftly  than  other  parts  :  the  air 
from  the  north  must,  therefore,  pass  over  portions  of  the 
earth  which  move  eastward  faster  than  itself,  and  it  will  be 
left  behind.  We  fiijdF,  then,  that  there  is  a  real  motion  from 
the  north,  and  at  the  same  time  an  apparent  motion  from  the 
east ;  these  two  motions  combined  make  the  direction  of  the 
wind  to  be  from  the  north-east.  A  similar  explanation  will 
show  why  the  southern  trade-wind  blows  from  the  south-east 
toward  the  north-west. 


SECTION   V. 

ON  VIBRATION. 

37.  Examples  of  vibration  are  abundant  among  the  mo- 
tions of  Solids,  Liquids,  and  Gases. 

Vibration  is  an  alternate  movement  back  and  forth.  (G. 
56,  80.) 

Examples.  —  If,  with  the  finger,  we  sink  one  scale-pan  of 
a  balance,  it  will  continue  to  pass  alternately  up  and  down 
over  the  same  path  for  a  long  time  after  the  finger  is  removed  : 
it  vibrates.  Or  if,  instead  of  pushing  it  down,  we  pull  the 
scale-pan  to  one  side,  and  then  release  it,  it  will  swing  back 
and  forth  for  a  long  time  :  this  alternate  motion,  to  and  fro, 
is  vibration.  Suppose  a  ball,  hung  by  a  fine  wire,  be  twirled 
by  the  fingers  so  as  to  twist  the  wire :  let  go  of  it,  and, 


NATURAL    PHILOSOPHY. 


93 


speedily  untwisting  the  wire,  it  will  go  on  for  a  time  twisting 
it  up  the  other  way.  The  ball  rotates,  first  in  one  direction 
and  then  in  the  other ;  and  this  alternate  motion  is  vibration. 

Or,  take  a  bent  glass  tube  ;  pour  water  into  it  until  the 
arms  are  two- thirds  full ;  tip  it  to  one  side,  and  then  suddenly 
bring  it  back  to  a  vertical  positition.  The  water  will  rise  and 
fall  in  the  arms  of  the  tube,  and  will  continue  this  alternate 
motion  up  and  down  for  some  time.  In  this  case  a  liquid 
vibrates. 

Gases  may  be  made  to  vibrate  in  the  same  way. 

Definition.  —  All  these  motions  are  alike  in  one  respect, 
different  as  they  seem  to  be  in  every  other.  It  is  in  every 
case  a  motion  to  and  fro,  or  alternately  back  and  forth. 
Motion  of  this  kind  is  called  VIBRATION. 


\ 


L— THE  PENDULUM. 

38.  The  pendulum  vibrates  under  the  influence  of  Gravita- 
tion and  Inertia.     Its  vibration  is  governed  by  three  laws  :  — 

1st,  The  time   of  one  vibration  ^ 

varies  as  the   square    root   of  the 
length  of  the  pendulum. 

2d,  The  time  of  one  vibration 
varies  inversely  as  the  square  root 
of  the  force  of  gravity. 

3d,  The  time  of  one  vibration  is 
independent  of  the  length  of  the 
arc  through  which  the  pendulum 
vibrates. 


The  Pendulum. — A  body  hang- 
ing from  a  fixed  point  under  which 
it  can  swing  freely  is  called  a  PENDULUM.  In  Fig.  48, 
the  pendulum  is  represented  as  a  ball  B,  hung  from  a 
point  A. 

If  this  ball  be  lifted  from  the  point  B  to  C,  and  then  re- 
leased from  the  hand,  it  will'  swing  back  and  forth  through 


94 


NATURAL   PHILOSOPHY. 


Fig.  49. 


the  arc  D  C,  going  a  less  and  less  distance,  until  finally  it 
will  stop  at  B.  Its  motion  from  one  end  of  its  arc  D,  to 
the  other  C,  is  ONE  VIBRATION  ;  and  the 
distance  B  C,  through  which  it  vibrates 
on  either  side  of  its  place  of  rest,  is 
called  the  AMPLITUDE  of  vibration. 

It  vibrates  under  the  Influence 
of  Gravitation  and  Inertia.  —  Sup- 
pose a  ball  at  M  (Fig.  49)  to  represent 
a  pendulum  hung  from  the  fixed  point 
C,  by  a  cord  M  C.  Now,  if  this  ball 
be  lifted  to  the  point  m,  and  for  a 
moment  held  there,  the  force  of  gravity 
will  act  upon  it  in  a  vertical  direction. 
We  will  represent  this  force  by  the  line  m  A,  and  resolve 
it  into  two  components  (see  p.  79),  shown  by  the  lines 
m  D  and  m  B.  The  force  m  B  acts  lengthwise  of  the  string 
without  effect  to  move  the  ball  ;  the  other  force,  m  D,  at 
right  angles  to  the  first,  will  pull  the  ball  toward  the  point 
M.  If  the  ball  is  allowed  to  fall  to  M,  its  inertia  will  carry 
it  be}^ond  that  point ;  but  gravitation  will  then  be  pulling  it 
back  with  just  the  same  power  that  it  exerted  to  pull  the  ball 
from  m  to  M.  It  will  rise  from  M  to  w,  a  distance  just  as 
far  from  M,  as  it  has  fallen  from  m.  It  will  there  stop,  and 
gravitation  will  bring  it  back  to  M,  while  its  inertia  will  carry 
it  up  to  m  ;  and  if  there  were  no  resistance  to  its  motion  it 
would  vibrate  for  ever  through  the  arc  n  m.  The  resistance 
of  the  air,  and  the  friction  of  the  cord  on  the  hook,  will  finally 
make  it  stop  at  M. 

The  first  Law.  —  If  two  pendulums  of  different  lengths 
(P  and  P',  Fig.  50)  be  made  to  vibrate  together,  the  short 
one  will  be  seen  to  vibrate  much  faster  than  the  other.  We 
learn  from  this  that  the  time  of  vibration  depends  on  the 
length  of  the  pendulum. 

Now,  let  us  make  one  pendulum  P  just  four  times  as 
long  as  the  other  P'.  With  a  watch  in  the  hand,  we  can 


NATURAL   PHILOSOPHY. 


95 


easily  count  the  number  of  vibrations  it  makes  in  one  minute  ; 

and  sixty  divided  by  this  number  shows  how  long  it  takes 

to  make  one  vibration.     In  the  same  way 

we  can  find  the  time  it  takes  the  shorter 

pendulum  to  make  one  vibration.     Doing 

this,  we  find  that  P  takes  twice  as  long  as 

P'  to  vibrate  once.     The  pendulum  being 

four  times  as  long,  the  time  of  vibration  is 

two  times  as  great.     Hence  the  time  of  one 

vibration  varies  as  the  square  root  of  the 

length  of  the  pendulum. 

Illustration.  —  The  length  of  a  pendu- 
lum to  vibrate  in  one  second  is  about  39.1 
inches  ;  to  vibrate  in  two  seconds,  it  must 
be  four  times  as  long ;  to  vibrate  in  one- 
half  a  second,  it  must  be  one-fourth  as 
long. 

The  second  Law.  —  B}'  calculating  the 
force  of  gravity  at  different  distances  above 
the  level  of  the  sea,  and  then,  b}T  experiment,  finding  the  time 
of  one  vibration  made  by  the  same  pendulum  at  those  places, 
it  will  be  found  that  the  time  of  one  vibration  varies  inversely 
as  the  square  root  of  the  force  of  gravity. 

The  third  Law.  —  Finally,  if  we  make  the  pendulum 
P  vibrate  in  a  large  arc,  and  find  the  time  of  one  vibration, 
and  then  make  it  vibrate  in  a  small  arc,  we  shall  find  the 
time  of  one  vibration  to  be  the  same.  The  pendulum  must 
vibrate  in  equal  times,  no  matter  whether  its  arc  be  large 
or  small.  In  other  words,  the  time  of  one  vibration  is  inde- 
pendent of  the  arc  through  which  the  pendulum  vibrates. 

This  third  law  is  absolutely  true  only  when  the  arcs  com- 
pared are  very  small.  Yet,  in  the  latitude  of  Paris,  it  is 
found  that  for  a  pendulum  whose  length  is  one  meter,  or 
39.37  inches,  the  time  of  one  vibration,  through  an  arc  of 
8°,  is  only  .000076  of  a  second  longer  than  if  its  arc  were 
infinitely  small. 


Fig.  50. 


96  NATURAL   PHILOSOPHY. 

39.  These  laws  apply  to  a  single  point  in   a  pendulum, 
called  the  center  of  oscillation. 

The  Center  of  Oscillation.  —  The  different  molecules 
of  a  pendulum  are  at  different  distances  from  the  point  of 
suspension,  and  hence  would  vibrate  in  different  times  if 
they  were  not  held  together  by  cohesion.  Although  they  are 
held  together,  and  must  all  move  at  once,  }*et  the  forces  that 
would  make  them  vibrate  differently  are  acting  just  the  same 
as  if  they  were  not.  The  upper  parts  of  the  pendulum  are 
trying  to  vibrate  faster,  and  must  be  pulling  the  lower  parts 
along ;  while  the  lower  parts  are  trying  to  vibrate  slower, 
and  must  be  pulling  the  upper  parts  back.  There  must  be 
some  point  in  the  pendulum  at  which  these  two  struggles  just 
balance  each  other.  This  point  will  vibrate  just  as  fast  as  if 
it  were  influenced  by  no  other  molecules  whatever.  A  point 
in  the  pendulum  which  vibrates  as  if  only  under  the  influence 
of  its  own  gravitation  and  inertia  is  called  the  CENTER  OF 
OSCILLATION.  The  center  of  oscillation  is  generally  a  little 
below  the  center  of  gravity  of  the  pendulum-ball. 

The  Laws  apply  to  this  Point.  —  The  three  laws,  ob- 
tained in  the  foregoing  paragraph,  apply  to  only  this  point, 
—  the  center  of  oscillation.  Indeed,  whenever  we  speak  of 
the  pendulum  we  refer  to  this  point.  By  the  length  of  a 
pendulum,  we  mean  the  distance  from  the  point  of  support  to 
the  center  of  oscillation  ;  and,  when  we  use  the  term  vibra- 
tion, we  refer  to  the  motion  of  this  one  point  of  the  pen- 
dulum. 

Huyghen's  Discovery.  —  The  centers  of  oscillation  and 
suspension  are  interchangeable.  If  a  pendulum  be  inverted, 
and  suspended  from  its  center  of  oscillation,  its  former  center 
of  suspension  becomes  its  new  center  of  oscillation,  and  its 
time  of  vibration  is  not  changed. 

40.  There  are  several  uses  of  the  pendulum ;    we    notice 
only  two  :  — 

1st,  It  is  used  to  measure  time. 


NATURAL   PHILOSOPHY.  97 

2d,  It  is  used  to  determine  the  form  of  the  earth.     (G. 

82.) 

Used  to  measure  Time.  —  The  vibrations  of  a  pend- 
ulum are  made  in  equal  times.  If,  then,  we  know  the  time 
of  one  vibration,  and  can  count  the  number  made,  we  know 
the  time  during  which  the  pendulum  vibrates. 

Now,  the  common  clock  is  an  instrument  in  which,  by 
weights,  friction  and  the  resistance  of  air  are  overcome,  so 
that  the  pendulum  shall  continue  its  motion,  and  by  which 
the  time  of  an}T  number  of  vibrations  is  at  the  same  time 
recorded  by  the  hands  moving  over  a  graduated  dial. 

Used  to  determine  the  Form  of  the  Earth.  —  The 
pendulum  has  been  used  to  determine  the  shape  of  the 
earth.  For  this  purpose,  pendulums  of  the  same  length  have 
been  made  to  vibrate  in  different  latitudes.  It  has  been 
found  that  the  time  of  one  vibration  is  less  and  less  as  the 
pendulum  approaches  the  poles  of  the  earth.  Now,  to  make 
the  vibrations  more  rapid,  the  force  of  gravity  must  increase  ; 
and,  if  this  force  is  stronger  toward  the  poles,  the  surface  of 
the  earth  must  be  nearer  the  center  of  the  earth  there  than 
at  the  equator.  The  polar  diameter  must,  therefore,  be 
shorter  than  the  equatorial  diameter,  and  the  shape  of  the 
earth  must  be  that  of  an  oblate  spheroid. 

II. -THE   VIBRATIONS   OP   CORDS. 

41.  The  vibrations  of  cords  are  due  to  the  action  of 
elasticity  and  inertia.  They  are  governed  by  three  laws  :  — 

1st,  The  number  of  vibrations  in  a  second  varies  inversely 
as  the  length  of  the  cord. 

2d,  The  number  of  vibrations  in  a  second  varies  directly 
as  the  square  root  of  the  weight  by  which  the  cord  is 
stretched,  or  its  tension. 

3d,  The  number  of  vibrations  in  a  second  varies  inversely 
as  the  square  root  of  the  weight  of  a  given  length  of  the  cord, 
(G.  259.) 


08  NATURAL   PHILOSOPHY. 

The  Vibration  of  Cords.  —  Let   a   cord   or   string   be 
stretched  between  two  fixed  points  (a  and  6,  Fig.  51).     By 


taking  hold  of  its  middle  point,  the  cord  ma}-  be  drawn  to 
one  side,  a  e  b.  Then  loose  it,  and  it  will  spring  back,  and 
go  an  equal  distance  on  the  other  side,  a  d  6,  then  return, 
and  so  continue  to  swing  rapidly  back  and  forth  until  it 
finally  stops  in  its  first  position,  a  c  b. 

The  motion  of  the  cord  from  e  to  d,  and  back  again,  is  a 
complete  vibration.  Its  motion  from  e  to  d  is  a  half- vibra- 
tion, or,  as  generally  called,  a  single  vibration.  The  distance 
either  side  of  its  line  of  rest  is  the  amplitude  of  vibration. 

Due  to  Elasticity  and  Inertia.  —  When  the  force  which 
stretches  the  string  into  the  position  a  e  b  is  withdrawn, 
elasticity  moves  it  back  to  its  first  position,  a  c  b;  and 
the  inertia  gained  by  this  motion  throws  it  forward  an 
equal  distance,  to  a  d  b.  The  elasticity  of  the  string  again 
pulls  it  back  to  the  position  a  c  6,  and  its  inertia  carries  it 
beyond  ;  and  thus,  under  the  joint  influence  of  elasticity  and 
inertia,  the  string  will  swiftly  vibrate,  its  amplitude  growing 
less  and  less,  on  account  of  resistance,  until  at  last  it  stops 
in  its  first  position. 

The  Laws  of  Vibration.  —  The  vibrations  of  cords  are, 
in  all  cases,  quite  too  rapid  to  be  counted ;  and  yet  it  will 
be  impossible  to  establish  any  laws  of  vibration,  unless  we 
can  find  the  number  of  vibrations  made  in  a  given  time. 
How  can  this  be  done  ?  l 

However  rapid  the  motion  of  the  cord  may  be,  the  swift- 
ness of  electricity  is  yet  greater  :  so  by  using  electricity  the 
cord  may  register  the  vibrations  which  it  makes. 

1  The  siren  will  be  described  in  the  chapter  on  sound :  it  seems  desirable  here 
to  make  the  cord  directly  register  its  own  vibrations,  so  that  thf  te'tr  of  vibration 
shall  stand  independent  of  sound. 


NATURAL   PHILOSOPHY. 


99 


The  apparatus  devised  for  this  purpose  by  the  author  is 
shown  in  Fig.  52. 

The  Electric  Register.  —  The  wire  V  is  stretched  over 
two  bridges  by  a  weight  w.  A  strip  of  paper  moistened 
with  a  mixture  of  potassium  iodide  and  starch  is  drawn 
rapidl}'  through  the  register  R.  Every  vibration  of  the  wire 
leaves  a  blue  dot  upon  the  paper,  and  the  number  of  these 
dots  made  in  a  second  can  be  easily  counted. 


Fig.  52. 

One  needs  to  know  something  about  electricity  to  clearly 
understand  its  action,  and  the  complete  description  of  the  ap- 
paratus 1  should  be  left  until  after  the  study  of  that  subject. 

1  The  wire  V,  a  time-measurer  P,  and  the  register  R,  are  included  in  the  same 
battery-circuit.  The  wire  is  enabled  to  open  and  close  the  circuit  by  means  of  a  fine 
steel  needle,  fixed  to  its  middle  point,  beneath  which  is  a  cup  of  mercury,  c,  the 
surface  of  which  is  so  nearly  in  contact  with  the  point  at  rest,  that  every  vibration 
of  the  wire  will  immerse  it  in  the  liquid  metal. 

For  the  measurement  of  time  a  pendulum  is  employed,  which  holds  the  circuit 
during  the  time  of  one  beat.  The  arrangement  for  this  purpose  is  represented  at 
P.  A  slender  fiber  is  fastened  to  the  pendulum-rod,  and  thence  reaches  over  to  the 
upper  end  of  a  light  bent  lever,  L.  This  lever  moves  freely,  and  is  in  conducting 
communication  with  a  binding  post,  n.  Beneath  the  lower  end  of  the  lever  is  a 
mercury  cup,  m,  in  metallic  connection  with  another  binding  post.  When  the 


100  NATX/RAL   PHILOSOPHY. 

The  first  Law.  —  The  wire,  V,  was  taken  4  feet  in 
length  :  stretched  by  a  weight  of  56  pounds  at  «?,  it  made  315 
complete  or  double  vibrations  in  3  seconds.  The  bridges 
were  then  placed  under  the  wTire  so  that  the  length  of  the 
vibrating  part  was  3  1'eet ;  it  then  made  420  vibrations  in 
3  seconds.  But  315  is  to  420  as  3:4.  We  see  that  when 
the  lengths  of  the  wire  are  as  4  :  3,  the  numbers  of  vibrations 
in  the  same  time  are  a&  3:4.  Hence  the  number  of  vibra- 
tions in  a  given  time  varies  inversely  as  the  lengths  of  the 
wire. 

The  second  Law.  —  The  wire  was  again  made  4  feet 
long,  and  the  weight,  10,  56  pounds.  The  vibrations  in  one 
second  then  numbered  105.  When  the  weight,  W,  was 
changed  to  14  pounds,  the  number  of  vibrations  in  one  sec- 
ond was,  in  some  experiments  52,  and  in  others  53.  The 
instrument  can  not  register  parts  of  a  vibration  ;  the  true 
number  is  evidently  between  52  and  53  :  we  may  call  it  52^. 
We  see  that  when  the  weights  are  56  and  14,  or  as  4  :  1,  the 
numbers  of  vibrations  made  in  a  second  are  105  and  52  J,  or 
as  2  :  1 .  Hence  the  number  of  vibrations  in  a  second  varies 
directly  as  the  square  root  of  the  weight  by  which  the  wire 
is  stretched. 

The  third  Law. —  The  wire  which,  being  4  feet  long, 
and  stretched  with  a  weight  of  56  pounds,  gave  105  vibra- 

heavy  pendulum  is  at  rest,  the  weight  of  the  lever  keeps  the  fiber  tense ;  and  the 
mercury  siirface  is  so  adjusted  as  to  be  exactly  in  contact  with  the  point  of  the  lever, 
a  most  vital  adjustment,  but  one  very  easily  made.  It  will  be  seen  that  the  pendu- 
lum, when  vibrating,  must  compel  the  lower  end  of  the  lever  to  be  alternately  in 
and  out  of  the  mercury  during  the  exact  time  of  one  vibration. 

The  record  of  the  vibrating  wire  is  made  in  the  register  R.  A  metallic  point,  a, 
presses  upon  a  strip  of  chemically-prepared  paper,  which  runs  over  a  platinum 
surface,  b.  The  pen,  and  the  platinum  beneath,  are  each  provided  with  a  binding 
post,  by  which  it  can  be  made  a  part  of  the  circuit.  The  paper  may  be  drawn 
through  by  the  hand  of  the  operator,  the  more  swiftly,  as  the  vibrations  are  more 
rapid. 

Let  the  circuit  be  continuously  closed  while  the  paper  is  in  motion,  and  a  con- 
tinuous colored  line  will  be  traced  by  the  pen,  a  ;  but  let  the  wire  vibrate,  and  elec- 
tric pulses  in  unison  with  it  will  traverse  the  paper,  leaving  a  series  of  dots  instead. 
If  the  pendulum  be  at  the  same  time  in  motion,  the  pulses  can  traverse  the  paper 
only  while  the  lever,  L,  is  in  mercury;  and  hence  a  group  of  dots  on  the  paper  will 
represent  the  vibrations  of  the  wire  in  the  unit  of  time. 


NATTJKAL  PHILOSOPHY^  1C! 

tions  a  second,  was  found  to  weigh  19.4  grin-is  -lo  the  (oo1: 
in  length.  Another  wire,  weighing  43  grains  to  the  foot, 
was  taken  of  the  same  length  and  tension  as  the  other  ;  and 
the  number  of  vibrations  in  one  second  was,  in  some  experi- 
ments 70,  and  in  others  71.  The  true  number  is  between 
these  :  call  it  70^.  Now,  the  weights  of  equal  lengths  of  the 
wire  being  19.4  :  43,  the  rates  of  vibrations  are  found  to 
be  105  :  70J ;  but  105  :  70  J  ::  \/43  :  \/!UA,  so  nearly  that 
we  may  infer  that  the  number  of  vibrations  a  second  varies 
inversely  as  the  square  root  of  the  weights  cf  equal  lengths 
of  the  wire. 

The  Kate  of  Vibration  is  invariable.  —  Thus  the  rate 
at  which  a  wire  or  cord  may  vibrate  is  fixed  by  the  length, 
weight,  and  tension  of  the  cord.  Every  piano-wire  vibrates 
with  a  certain  rapidity ;  and  no  human  power  can  change  it 
so  long  as  the  length,  weight,  and  tension  of  the  wire  remain 
the  same. 

III.— VIBRATIONS   OF  OTHER  BODIES. 

Of  a  Bell.  —  In  Fig.  53  we  are  shown  a  bell-shaped  glass 
vessel  with  a  little  pendulum-ball  hanging  beside  it.  By 
drawing  a  violin-bow  across  the  edge  of  this  bell  we  make 
the  glass  vibrate  ;  and  we  shall  know  that  the  vibrations  are 
made,  because  the  little  pendulum-ball  will  fty  back  and  forth 
with  a  violent  clatter.  The  edge  of  the  glass,  springing  back 
and  forth,  puts  the  ball  in  motion. 

This  is  one  of  the  man}'  cases  of  vibration  in  which  the 
motion  is  too  delicate  to  be  seen,  and  the  existence  of  which 
would  not  be  known  if  some  way  had  not  been  discovered  by 
which  to  make  the  vibrations  show  themselves.  Cases  of 
such  invisible  vibrations  are  very  common.  In  fact,  they 
already  exist  or  may  be  produced  in  almost  ever}7  solid  body 
we  can  see  around  us. 

Of  Water. — Let  the  glass  vessel  (Fig.  53)  be  almost 
filled  with  water,  and  the  bow  then  drawn  across  its  edge. 
The  fluid  will  be  thrown  into  violent  commotion.  Hosts  of 


102 


NATURAL  PHILOSOPHY. 


little  wavelet ptoiiil. be-  thrown  up  and  down  in  quick  succession 
upon  its  surface,  the  water  being  thrown  into  vibration  by 
the  vibration  of  the  glass. 

By  skillfully  drawing  the  bow  these  wavelets  may  be 
brought  into  four  and  sometimes  into  six  beautiful  groups 
separated  from  each  other  b}'  portions  of  water  which  seem  to 
be  at  rest.  Not  many  effects  as  fine  can  be  so  easily  produced. 


Fig.  53. 

Of  Air.  —  The  air  is  so  elastic  that  it  jields  to  every 
force,  even  the  very  slightest,  and  then  afterward  springs 
back  again.  On  this  account  it  is  in  a  state  of  vibration  all 
the  time.  We  can  not  stir  a  hand  without  causing  the  air 
to  vibrate.  It  is  made  to  tremble  by  every  breath,  and  it 
quivers  at  every  motion  of  our  lips. 


NATURAL  PHILOSOPHY. 


103 


A' 


SECTION   VI. 
ON   UNDULATIONS. 

42.  Vibrations  may  be  transmitted  from  point  to  point  in 
the  same  mass. 

The  motion  then  becomes  an  Undulation.      {A.  475,  534.) 

Transmission  along  a  Cord.  —  Let  a  heavy  cord,  or 
better  still,  an  India-rubber  tube  (A  B,  Fig.  54),  several 
feet  long,  be  fastened  at  one  end 
to  the  wall  or  ceiling  of  the  room. 
Take  hold  of  the  free  end  with  one 
hand,  and,  by  a  sudden  blow  with 
the  other,  push  the  part  B  C  aside, 
as  shown  in  the  figure.  The  little 
hillock  thus  formed  will  run  swiftty 
up  the  tube  to  A,  and  then  quickly 
down  to  the  hand  again.  By  care- 
fully noticing  the  motion,  it  will  be 
seen  that  while  the  hillock  running 
up  to  A  is  on  one  side  of  the  cord 
or  tube,  that  which  returns  to  the 
hand  is  on  the  other.  Having  gone 
to  the  top,  as  seen  at  A',  it  turns 
as  seen  at  A'',  and  then  comes  down. 
Nor  does  it  then  stop :  it  will  again 
and  again  run  up  and  down  the  tube 
until,  the  height  of  the  hillock  grow- 
ing less  and  less,  it  finally  disap- 
pears. 

The    Motion    appears    to    be 
Lengthwise  of  the  Tube.  —  It  is 
interesting  and  important  to  notice 
that  while  the  motion  appears  to  be  lengthwise  of  the  cord 
or  tube,  the  only  real  motion  of  the  parts  is  back  and  forth, 


Fig.  54. 


104 


NATURAL   PHILOSOPHY. 


across  their  first  position.  Each  point  of  the  cord  is  put  in 
motion  a  little  later  than  the  one  before  it,  and  the  vibration 
progresses  along  the  cord. 

Definition.  —  The  transmission  of  a  vibration  through 
successive  portions  of  a  mass  is  an  UNDULATION. 

A  Wave.  —  By  starting  several  hillocks,  one  after  the 
other  quickry,  the  whole  cord  may  be  thrown  into  a  series  of 
hills  and  valleys,  as  shown  in  Fig.  55.  In  this  case  the 
A  motion  between  B  and  D,  consisting  of 
two  parts,  on  opposite  sides  of  the  mid- 
dle line,  is  called  a  WAVE.  Two  waves 
are  represented  in  the  figure. 

Phase.  —  When  the  cord  is  in  mo- 
tion as  shown  in  Fig.  55,  the  two  points 
B  and  D  are  moving  exactly  alike. 
They  are  moving  in  the  same  direction 
and  with  the  same  velocity.  This  is 
not  true  of  any  other  points  between 
these.  Two  points  in  a  wave  which 
move  in  the  same  direction  and  with 
the  same  velocity  are  said  to  be  in  the 
same  phase. 

Two  points  moving  in  opposite  direc- 
tions with   the   same   velocity   are    in 
ff  opposite  phases. 

Wave -Length.  —  The  distance  be- 
tween two  points  in  the  same  phase  is 
the  LENGTH  of  the  wave. 

Period.  —  The  time  required  for  any 
particle  in  the  wave  to  make  one  vibra- 
tion is  the  PERIOD.  The  undulation 
advances  jus^  one  wave-length  in  the 
same  time. 

Interference  of  Waves.  —  By  skillfully  timing  the  im- 
pulses of  the  hand,  the  hillocks  on  both  sides  of  the  middle 
line  in  Fig.  55  may  be  made  to  turn  themselves  over  at 


£ 

Fig.  56. 


NATURAL  PHILOSOPHY.  105 

the  same  time.  In  that  case,  the  tube  will  present  the 
appearance  shown  in  Fig.  56  ;  the  points  a,  6,  c,  being 
almost  stationary,  while  the  parts  between  are  swinging  to 
and  fro  across  the  middle  line,  making  vibrations,  just  as  if 
they  were  separate  cords. 

The  points  which  appear  to  be  at  rest  are  called  NODES, 
while  the  vibrating  parts  between  them  are  called  VENTRAL 
SEGMENTS. 

At  each  node  two  waves  meet,  in  opposite  phases,  one 
going  up  the  cord,  the  other  coming  down.  They  pull  that 
point  equally  in  opposite  directions;  for  this  reason  it  remains 
at  rest.  Both  pulses  act  in  the  segments  also,  but  not  with 
equal  strength;  and  the  cord  moves  in  the  direction  of  the 
stronger. 

The  mutual  action  of  two  or  more  undulations  upon  the 
same  mass  at  once  is  called  INTERFERENCE. 

43.  Undulatory  motion  is  illustrated  by  Water-waves. 
Two  sets  of  water-waves  may  interfere  with  each  other, 
and  produce  a  single  set  different  from  either. 

Water -Waves.  —  Let  a  pebble  be  tossed  into  the  water 
of  a  lake  or  pond,  and  the  tranquil  surface  will  be  carved 
into  a  series  of  circular  ridges  and  furrows,  which,  grow- 
ing gradually  larger  and  larger,  finally  break  against  the 
shore.  The  motion  appears  to  be  in  all  directions  out- 
ward from  the  pebble ;  but  the  little  sticks  and  straws  that 
may  be  resting  upon  the  water  at  the  time  tell  us,  by  their 
dancing,  that  the  real  motion  of  the  water  is,  like  their  own, 
a  motion  only  up  and  down. 

A  wave  of  water  consists  of  two  parts,  —  a  ridge  and  a 
furrow. 

Water  -Waves  may  interfere.  —  Let  two  sets  of  water- 
waves  be  started  at  the  same  time,  by  dropping  two  pebbles 
at  a  little  distance  from  each  other.  The  two  sets  of 
growing  circles  very  soon  cross  each  other,  and  then  the 
smooth  surface  of  the  water  will  be  cut  U.D  into  a  curious 


lOb'  NATURAL  PHILOSOPHY. 

confusion  of  dancing  hummocks.  Some  of  these  hummocks 
will  be  twice  as  high  as  the  ridges  of  either  set  of  waves, 
while  others  will  just  lift  their  heads  above  the  original  sur- 
face of  the  water.  When  two  sets  of  waves  are  thrown 
together,  they  are  said  to  interfere. 

But  wiry  are  the  hummocks  of  such  different  heights  ?  It 
is  clear  that  when  two  ridges  come  together  their  heights  will 
be  united,  and  the  height  of  the  hummock  will  be  the  sum 
of  their  sepajate  heights.  But  when  the  ridges  of  one  set 
enter  the  furrows  of  the  other,  the  height  of  the  resulting 
hummock  will  be  equal  to  their  difference.  Now,  as  the 
waves  are  running  across  each  other,  the  hummocks  must  be 
of  various  heights,  limited  on  the  one  hand  by  the  sum  of  the 
heights  of  the  ridges  of  the  two  sets,  and  on  the  other  by 
their  difference. 

The  Principle  of  Interference.  —  Any  number  of  waves 
may  traverse  the  same  medium  at  the  same  time.  They  are 
equivalent  to  a  single  compound  wave  in  which  the  motion  at 
any  point  is  the  algebraic  sum  of  the  motions  which  the 
component  waves  impart. 

44.  The  undulations  in  air  consist  of  alternate  Rarefac- 
tions and  Condensations.  In  free  air  the  waves  travel  out- 
ward from  their  source  in  eveiy  possible  Direction.  Different 
sets  must  be  constantly  interfering.  (A.  477,  478.) 

Alternate   Rarefactions   and   Condensations.  —  We 

have  seen  (see  p.  44)  how  easilj-  air  ma}'  be  compressed,  and 
with  what  promptness  it  springs  back  to  its  former  volume 


Fig.  57. 


when  the  compressing  force  is  removed.  Now,  suppose  that 
near  to  one  end  of  a  long  tube  is  a  piston,  P  (Fig.  57). 
By  suddenly  pushing  this  piston  forward  to  F,  and  then 


NATURAL   PHILOSOPHY.  107 

instantly  pulling  it  back,  the  air  in  the  whole  length  of  the 
tube  will  be  put  in  motion.  Let  us  analyze  this  motion. 

When  the  piston  moves  from  P,  it  crowds  the  air  before  it ; 
and,  when  it  has  reached  P',  this  crowding  effect  will  have 
gone  forward  to  some  point  A,  more  or  less  distant.  The 
space  I"  A  is  then  filled  with  condensed  air.  When  the 
pressure  of  the  piston  is  removed,  the  condensed  air  springs 
back.  It  springs  both  ways,  backward  against  the  piston, 
and  forward  against  the  air  at  A.  By  its  pressure  against 
the  air  at  A,  the  air  in  the  space  A  B  will  be  condensed. 
The  next  moment  this  air  expands,  and,  pressing  both  ways, 
condenses  the  air  B  C  in  front  of  it,  and  also  the  air  A  P 
behind  it.  These  two  portions  will,  in  this  wa}T,  be  con- 
densed, while  the  air  A  B  will  be  rarefied.  The  next  instant 
these  condensed  portions  spring  back,  and  become  rarefied, 
while  the  rarefied  portion  A  B,  and  at  the  same  time  another 
part  be}rond  C,  will  be  condensed.  The  air  is  in  this  way 
thrown  into  a  series  of  condensed  and  rarefied  parts,  alter- 
nately springing  back  and  forth  in  the  direction  lengthwise 
of  the  tube.  We  need  only  add,  that  there  is  no  sudden 
transition  from  condensed  to  rarefied  air  at  the  points  A,  B, 
and  C.  The  mobility  of  air  will  not  permit  this.  At  the 
middle  of  the  condensed  part  the  condensation  is  greatest, 
while  at  the  middle  of  the  rarefied  part  is  the  greatest  rare- 
faction, and  between  these  points  the  change  is  gradual. 

A  wave  of  air  consists  of  two  parts,  —  a  condensation  and 
a  rarefaction. 

Waves  in  free  Air  go  in  all  Directions.  —  The  walls 
of  a  tube  confine  the  air,  and  compel  the  waves  to  flow  in 
the  direction  of  its  length.  In  free  air  the  case  is  different. 
Every  impulse  by  which  the  atmosphere  at  any  point  is  sud- 
denly 'condensed  or  rarefied  is  the  center  from  which  air- 
waves go  outward  in  all  directions. 

Let  a  few  grains  of  gunpowder  be  exploded.  A  little 
sphere  of  air  at  the  point  where  the  explosion  occurs  will 
be,  for  the  moment,  rarefied,  while  by  its  pressure  a  shell  of 


108  NATURAL    PHILOSOPHY. 

air  outside  of  it  will  be  condensed.  This  condensed  air, 
instantly  springing  back,  condenses  the  air  on  both  sides 
of  it,  and  itself  becomes  rarefied.  The  waves  will  thus 
travel  outward  from  the  center,  until  the  whole  body  of  air  in 
the  room  is  thrown  into  a  scries  of  concentric  shells,  alter- 
natch  condensed  and  rarefied. 

How  constant  and  complicated  must  be  these  vibrations 
of  the  air!  Every  sudden  and  local  putt'  of  wind,  every  for- 
cible breath  exhaled  from  the  lungs  ;  the  fall  of  every  stick 
and  stone, — all  these  are  the  sources  of  as  many  differ- 
ent sets  of  waves  spreading  in  all  directions,  darting  across 
and  through  each  other,  too  delicate  to  be  seen  or  felt,  but 
presenting  to  the  mind  a  scene  of  activity  far  exceeding  the 
power  of  the  senses  to  appreciate. 

Different  Sets  interfere.  —  Suppose  two  sets  of  air- 
waves come  together:  if  their  condensed  parts  coincide,  a 
single  set  will  be  formed  whose  condensations  are  greater 
than  either.  If  the  condensed  parts  of  one  set  coincide  with 
the  rarefied  parts  of  the  other,  there  will  be  a  single  set 
whose  condensations  are  less  than  either.  In  the  first  case. 
if  the  two  sets  are  equal,  the  resulting  waves  will  be  doubled  ; 
if,  in  the  other  case,  the  two  sets  are  equal,  they  will  destroy 
each  other,  leaving  the  air  without  waves. 

Transverse  and  longitudinal  Vibrations.  —  In  the 
water-wave  the  water  itself  moves  vertically  while  the  wave 
moves  horizontally.  Whenever  the  parts  of  a  medium  vibrate 
at  right  angles  to  the  direction  of  the  wave,  the  vibration  is 
TRANSVERSE. 

In  the  air-wave  the  molecules  of  air  move  back  and  forth 
lengthwise  of  the  wave  itself.  All  such  vibrations  are 
LONGITUDINAL. 


NATURAL   PHILOSOPHY.  109 

SECTION   VII. 

REVIEW. 
I.— SUMMARY    OF   PRINCIPLES. 

Attraction  and  repulsion  in  one  form  or  another  determine 
the  condition  of  rest  or  motion  of  masses  and  of  molecules. 

If  a  body  could  be  acted  on  by  a  single  force,  its  motion 
would  be  in  a  straight  line  unchanged  for  ever. 

When  forces  act  together,  each  does  the  same  amount  of 
work  as  it  would  if  acting  alone. 

An  impulsive  force  alone  will  produce  uniform  velocity. 

A  constant  force  alone  will  produce  uniformly  accelerated 
velocit}'. 

Curved  motion  is  produced  by  the  action  of  two  forces,  one 
of  which,  at  least,  is  constant. 

The  alternate  action  of  two  opposite  forces  produces  vibra- 
tion. 

The  transmission  of  a  vibration  from  point  to  point  in  a 
body  is  an  undulation. 

II.  — SUMMARY   OF  TOPICS. 

23.  Application  of  the  fundamental  ideas  to  explain  the 
production  of  motion. 

24.  Newton's  first  law.  —  Second  law.  —  Third  law. 

25.  Velocity  defined.  —  Uniform  velocity. — An  impulsive 
force.  — Uniform  motion  due  to  an  impulse.  — Space = time 
X  velocity. 

26.  A  constant  force.  —  Uniformly  accelerated  motion. — 
Difficulties  in  the  way  of  experiment.  —  Overcome   by  At- 
wood's  machine. 

27.  Experimental  proof  of  the  first  principle.  —  Experi- 
mental proof  of    the   second   principle. — Analysis   of  the 
motion   of  a   falling   body  by  these  principles.  —  Tabulate 
the  results.  —  From  the  table  obtain  laws.  —  Also  formulas. 


110  NATURAL   PHILOSOPHY. 

—  Acceleration   defined.  —  The   value   of  g.  —  Solution   of 
problems  by  the  formulas. 

28.  If  a  body  be  acted  on  by  two  forces.  — Acting  in  the 
directions  of  adjacent  sides  of  a  parallelogram.  —  They  are 
equivalent  to  a  single  force.  — The  resultant  ma}'  be  found. 

29.  An}*  force  may  be  resolved.  — To  find  the  component 
in  a  given  direction. 

30.  Two  forces  in  the  same  direction. — Point  of  appli- 
cation. —  The  weight  of  a  body.  —  The  center  of  gravity.  — 
The  line  of  direction.  —  Principle  of  stability. 

31.  Curved   motion. — Requires   action   of    at   least   two 
forces.  — One  of  which  is  constant.  — The  central  forces.  — 
Centripetal   force.  —  Centrifugal   force.  —  Experiments.  — 
Illustrations.  — Projectiles.  — Range. 

32.  The  velocity  of  a  jet  of  water. — It  depends  on  the 
distance  of  the  orifice  below  the  surface.  — Calculated  by  a 
formula. 

33.  To  calculate  the  quantity.  — Example. 

34.  The  quantity  in  practice   less   than  in  theory. — In- 
creased by  using  tubes. 

35.  No  lateral  pressure  by  a  vertical  stream.  — Motion  of 
the   adjacent  air.  —  Applied  to  produce  a  blast.  —  Applied 
also  to  produce  a  vacuum. 

36.  Wind. — The    trade-winds.  —  Due   to   heat   and  the 
rotation  of  the  earth. 

37.  Examples  of  vibration. — Definition. 

38.  The   pendulum. — Vibrates    under   the    influence   of 
gravity  and  inertia.  —  The  first  law.  —  The  second  law.  — 
The  third  law. 

39.  The   center  of  oscillation. — The   laws  apply  to  this 
point.  —  Huyghen's  discovery. 

40.  The  pendulum  used  to  measure  time.  — To  determine 
the  form  of  the  earth. 

41.  The  vibration  of  cords.  —  Due  to  elasticity  and  inertia. 

—  The  laws  of  vibration.  —  First  law.  —  Second  law.  —  Third 
law.  —  Rate  invariable.  —  Vibrations  of  a  bell.  — Of  water. 
Of  air. 


NATURAL  PHILOSOPHY.  Ill 

42.  Transmission  of  vibration  along  a  cord.  — The  motion 
appears    to    be   lengthwise.  —  Definition   of    undulation.  — 
A  wave.  —  Phase.  —  Wave-length.  —  Period.  —  Interference 
of  waves. 

43.  Water-waves. — May    interfere.  —  The    principle    of 
interference. 

44.  Alternate  rarefaction  and  condensation  of  air.  —  Waves 
in  free  air  go  in  all  directions. — Different  sets  interfere. — 
Transverse  and  longitudinal  vibrations. 

III. —PROBLEMS. 
Illustrating  the  Laws  of  Motion. 

1 .  A  body  moves  uniformly  over  a  distance  of  780  feet 
with  a  velocity  of  5  feet  a  second  :  in  what  time  did  it  go  ? 

Ans.  156  seconds. 

2.  Under  the  influence  of  an  impulsive  force,  a  body  moves 
at  the  rate  of  25  feet  a  second  :  how  far  will  it  go  in  one 
minute  ? 

3.  A  stone  dropped  from  the  top  of  a  tower  struck  the 
ground  in  4  seconds  :  how  high  is  the  tower  ? 

Ans.  25 7 J  feet. 

4.  If  the  tower  were  257^-  feet  high,  with  what  velocity 
would  a  stone  strike  the  ground?  Ans.  128§  feet. 

5.  If  the  velocity  of  the  stone  should  be  128f  feet  a  sec- 
ond, how  long  a  time  had  it  been  falling?    Ans.  4  seconds. 

6.  A  body  falls  4  seconds  :  how  far  does  it  go  in  the  fourth 
second?  Ans.  112^  feet. 

7.  Under  the  influence  of  a  constant  force,  a  body  moves 
3  feet  the  first  second :  how  far  will  it  go  in  5  seconds  ? 

Ans.  75  feet. 

8.  A  body  is  falling  toward  the  earth ;  it  is  at  the  same 
time  moving  horizontally  under  the  influence  of  a  constant 
force  which  made  it  go  10  feet  in  the  first  second  :  how  far, 
horizontally,  did  it  go  in  8  seconds?  Ans.  640  feet. 

9.  How  far  did  it  fall  in  the  same  time? 

Ans.  1,029£  feet. 


112  NATUKAL   PHILOSOPHY. 

10.  With  what  velocity  did  it  strike  the  ground? 

Ans.  2571  feet. 

11.  What  velocity  did  it  gain  in  a  horizontal  direction? 

Ans.  160  feet. 

12.  How  far  did  it  go  horizontally  in  the  fifth  second? 

Ans.  90  feet. 

13.  How  far  did  it  fall  in  the  fifth  second? 

Ans.  144  j  feet. 

14.  Under  the  influence  of  a  constant  force,  a  body  goes 
12  feet  in  the  first  3  seconds  :  how  far  does  it  go  in  18  sec- 
onds? Ans.  432  feet. 

15.  A  ball  is   thrown   directly  upward,   starting  with   a 
velocity  of  96^  feet :  to  what  height  will  it  rise? 

Ans.  144|  feet. 

The  motion  of  this  ball  thrown  upward  will  be  retarded 
by  gravitation  in  exactly  the  same  ratio  that  it  is  accelerated 
in  falling  to  the  ground  again.  The  height  to  which  it  rises 
is  the  same  as  that  from  which  it  falls.  This  problem  may 
be  solved  exactly  as  if  the  question  were  :  From  what  height 
would  the  ball  fall  to  gain  a  velocity  of  96J  feet  a  second? 

16.  A  ball  is  shot  upward  with  a  velocit}T  of  386  feet: 
how  long  will  it  continue  to  rise?  Ans.  12  seconds. 

17.  How  high  does  it  go?  Ans.  2,316  feet. 

18.  How  long  does  it  remain  in  the  air? 

Ans.  24  seconds. 

19.  How  far  does  it  rise  in  the  last  second  of  its  ascent? 

Ans.  16TV  feet. 

20.  How  far  does  it  fall  in  the  last  second  of  its  descent? 

Ans.  3691J  feet. 

21.  Suppose  the  large  weights  of  Atwood's  machine  to  be 
each  23  J  ounces,  and  the  weight  of  the  small  bar  to  be  one 
ounce.     We  find,  by  experiment,  that  the  weight  and  bar  go 
4  inches   in   the   first    second :  what  is   the  acceleration  by 
gravity?  or,  in  other  words,  what  is  the  value  of  g? 

Ans.  32  feet. 
In  this  case,  the  whole  weight  moved  by  the   force   of 


NATURAL   PHILOSOPHY.  113 

gravitation  on  the  bar  is  23  J  +  23J  +  1  =  48  ounces.  It  is 
clear  that  48  ounces  will  move  only  -£$  as  far  in  one  second 
as  one  ounce  moved  by  the  same  force  freely.  Hence  4  x 
48  =  192  inches  would  be  the  distance  the  bar  would  fall 
freely  in  the  first  second.  This  distance  is  equal  to  16  feet. 
When  the  experiment  is  accurately  made,  at  the  level  of  the 
sea,  it  is  found  to  be  16T^  feet.  The  acceleration  is  twice 
this  distance. 

22.  An  orifice  is  made  near  the  bottom  of  a  dam  at  a  dis- 
tance of  16  feet  below  the  level  of  the  water:    with  what 
velocity  does  the  water  issue?  Ans.  32. 

23.  How  large  an  orifice  must  be  made  in  a  dam  10  feet 
below  the  level  of  the  water  in  order  to  supply  100  cubic 
feet  of  water  a  second  ? 

24.  Water  issues  from  the  muzzle  of  a  hose  directed  up- 
ward with  a  velocity  of  100  feet  a  second :  to  what  height 
would  it  be  thrown  if  there  were  no  friction  nor  resistance 
of  air? 


114 


NATURAL  PHILOSOPHY. 


CHAPTER  IV. 
ON  ENERGY. 


SECTION   I. 

ON  DEFINITIONS  AND  MEASUREMENTS. 

WHENEVER  a  body  is  put  in  motion,  as  when  a  stone  is 
thrown  from  the  hand,  it  will  con- 
tinue to  move  for  a  while,  going  more 
and  more  slowly,  until  it  finally  stops. 
To  explain  this  fully,  requires  us  to 
notice  several  things.  Let  us  sup- 
pose it  to  be  an  arrow  shot  vertically 
upward  (Fig.  58)  :  we  must  notice 

The  Mass  of  the  arrow  ; 

The  Force  which  throws  it ; 

The  Work  done  in  sending  it  to 
the  top  of  its  path  ; 

The  Energy  expended  in  doing 
this  work. 

45.  Mass  is  the  quantity  of  matter 
in  a  bod}*.  Its  value  is  found  by 
dividing  the  weight  of  the  body  by 
the  acceleration  caused  by  gravity. 


That  is,  m  =  -. 

i/ 


(1.) 


Fig.  58. 


Mass  and  its  Measure.  —  The 

quantity  of  matter  contained    in   a 
body  is  always  the  same.    Wherever 


NATURAL  PHILOSOPHY.  115 

the  body  may  be  upon  the  earth's  surface,  or  even  if  it  could 
be  alone  in  space,  it  would  contain  the  same  quantity  of 
matter  ;  or,  in  other  words,  its  mass  would  not  change. 

Not  so  with  the  weight  of  the  bod3\  Weight  is  caused  by 
the  earth's  attraction,  and  must  change  as  this  attraction 
varies.  The  same  body  weighs  less  when  the  force  of 
gravity  is  weaker,  as  in  higher  latitudes,  for  example  ;  and  if 
we  imagine  a  body  alone  in  space  with  none  other  to  attract 
it,  it  has  no  weight  at  all.  Clearly  mass  and  weight  are  very 
different  things. 

But,  if  the  weight  of  a  body  at  any  place  is  divided  by  the 
force  of  gravity  at  the  same  place,  the  quotient  will  be  the 
same  wherever  the  body  may  be,  because  the  weight  does 
vary  exactly  as  the  force  of  gravity  varies.  This  quotient  is, 
then,  a  numerical  value  which  is  the  same  for  the  same  body 
anywhere,  and  hence  it  may  represent  the  mass  of  it. 

weight       to      ,,.A 

Mass  = %— = -.     (1.) 

gravity      g 

46.  Force  is  that  which  tends  to  produce,  to  destroy,  or  in 
any  way  to  change,  the  motion  of  a  body. 

Its  value  is  found  by  multiplying  the  mass  of  the  body  on 
which  it  acts  by  the  velocity  which  it  imparts. 

That  is,  f=mxv.     (2.)      (G.  28,  29  ;  A.  126,  127.) 

Force  and  its  Measure. — To  move  a  mass  of  rock  re- 
quires a  certain  amount  of  force.  If  the  mass  were  twice 
or  thrice  as  great,  it  would  require  twice  or  thrice  as  much 
force  to  move  it  with  the  same  velocity,  which  shows  us  that 
force  varies  directly  as  the  mass  which  it  puts  in  motion. 

But  to  move  that  same  rock  twice  as  fast  would  also  need 
twice  as  much  force  ;  or,  in  other  words,  the  force  varies 
directly  as  the  velocity  which  it  produces. 

The  product  of  these  two,  mass  and  velocit}r,  represents 
the  force. 

Force  =  mass  X  velocit}'  =  m  x  v.     (2.) 

If  a  constant  force  is  acting,  then  the  acceleration  is  the 
velocity  which  is  represented  by  v  in  this  calculation. 


116  NATURAL  PHILOSOPHY. 

The  force  which  sends  the  arrow  would  be  measured  by 
the  product  of  the  mass  of  the  .arrow  by  the  velocity  with 
which  it  leaves  the  bow. 

47.  To  overcome  resistance,  of  whatever  kind,  is  Work. 

Its  value  is  found  by  multiplying  the  weight  of  the  body 
by  the  vertical  height  through  which  the  force  applied  would 
lift  it. 

That  is,  r  =  tv  s.     (3.)      (G.  61  ;  A.  175,  177.) 

Work.  —  The  wrord  u  work  "  is  used  in  science  very  much 
as  it  is  elsewhere.  It  is  applied  to  whatever  requires  an  effort. 
In  science  its  meaning  is  more  precise  than  in  common  use. 
To  cany  weights  up  stairs  is  work,  and  if  the  weights  are 
heavy  we  call  it  hard  work.  But  in  science  we  measure  it, 
and  give  a  numerical  value  to  the  work  which  is  done. 

The  Unit.  —  Let  us  suppose  each  step  of  the  stairs  to  be 
just  one  foot  high.  Now,  if  I  lift  a  one-pound  weight  from 
the  floor,  and  place  it  on  the  first  step,  I  do  a  little  work  ;  and 
I  should  do  exactly  the  same  amount  of  work  each  time  if  I 
were  to  do  it  over  and  over  again.  Since  I  have  lifted  one 
pound  to  the  height  of  one  foot,  we  may  call  the  little  work 
done  a  FOOT-POUND.  This  is  the  unit  in  which  work  is 
measured.  A  foot-pound  is  the  work  done  in  lifting  one 
pound  to  the  height  of  one  foot. 

If  I  have  carried  the  pound  up  ten  steps  of  the  stairs,  each  a 
foot  high,  how  much  work  have  I  done  ? 

Ans.  10  foot-pounds. 

If  I  have  lifted  a  weight  of  two  pounds  up  one  step,  how 
much  work  have  I  done?  Ans.  2  foot-pounds. 

If  I  have  lifted  two  pounds  up  ten  steps,  how  much  work 
has  been  done  ?  Ans.  20  foot-pounds. 

Rule.  —  To  find  the  numerical  value  of  work,  multiply  the 
weight  lifted,  by  the  height  to  which  it  is  raised.     Let  work 
be  represented  by  r,  and  height  by  s :  then, 
r  =  w  X  s.     (3.) 

The  work  done  in  throwing  the  arrow  upward  is  found  by 


NATURAL   PHILOSOPHY.  117 

multiplying  the  weight  of  the  arrow  b}r  the  height  to  which  it 
flies. 

The  French  Unit.  —  In  the  French  system  the  unit  of 
work  is  called  the  kilogram-meter :  it  is  the  amount  of  work 
done  in  lifting  a  body  weighing  one  kilogram  to  a  height  of 
one  meter. 

Work  is  independent  of  Time.  —  For,  whether  I  lift 
my  weights  to  the  top  of  the  stairs  in  one  minute  or  in  twent}' 
minutes,  the  same  amount  of  work  is  done. 

To  measure  Work  in  other  Directions.  —  But  how 
can  work  be  measured  in  foot-pounds  if  the  body  is  not  lifted 


'     Fig.  59. 

vertically?  In  Fig.  59  we  see  a  cask  of  merchandise  being 
drawn  up  the  stairwa}'.  Perhaps  it  weighs  two  hundred 
pounds  ;  and  we  ask  how  much  work  is  done  in  bringing  it 
to  the  top  ?  It  is  easy  to  see  that  when  it  has  been  drawn 
from  the  floor  to  the  platform  along  the  steps,  it  has  been 
lifted  only  through  the  vertical  distance  from  the  floor  up  to 
the  platform  on  which  the  laborers  stand.  If  the  height 
of  the  platform  above  the  floor  is  ten  feet,  then  two  hundred 
pounds  lifted  ten  feet  is  equal  to  two  thousand  foot-pounds. 


118  NATURAL  PHILOSOPHY. 

And  this  is  the  amount  of  work  done  in  rolling  the  cask  up 
the  stairs. 

And  so,  when  work  is  done  in  any  direction  whatever,  we 
ma}'  find  to  what  vertical  height  the  body  would  be  lifted 
against  gravity  with  the  same  amount  of  work  ;  and  then  the 
weight  of  the  body  multiplied  by  this  height  is  the  amount 
of  work  done. 

48.  By  energy  we  mean  the  ability  to  do  work. 
The  energy  of  a  body  in  motion   is   found   by  multiply- 
ing one-half  its  mass  by  the  square  of  its  velocity. 


That  is,  k  =  ~.     (4.)      (O.  63  ;  A.  179-181.) 

i/ 

Energy.  —  When  a  nail  is  driven  into  wood,  the  moving 
hammer  does  the  work.  It  is  true,  the  abilit3T  to  do  this 
work  is,  at  first,  in  the  hand  which  wields  the  hammer;  but 
the  hand  gives  this  ability  to  the  hammer,  and  it  is  the  ham- 
mer that  final!}'  drives  the  nail.  The  hammer  in  motion  is 
able  to  overcome  the  resistance  of  the  wood,  and  this  ability 
to  do  work  is  its  ENERGY.  A  heavier  blow  would  drive  the 
nail  deeper,  because  the  hammer  would  be  endowed  with 
greater  energy. 

A  stone  thrown  vertically  upward  rises  in  opposition  to 
the  force  of  gravity.  In  throwing  it  to  a  greater  height,  more 
work  is  done  ;  and,  if  you  can  project  it  higher  than  I  can,  it 
is  because  there  is  more  energy  in  your  hand  than  in  mine. 

Every  moving  body  is  endowed  with  energy. 

Depends  on  Mass  and  Velocity.  —  A  falling  mass  of 
rock  possesses  great  energy;  it  shows  it  by  crushing  the 
obstacles  in  its  pathway.  A  flying  bullet  also  has  great 
energy  ;  it  shows  it  by  piercing  whatever  it  may  strike. 

Now,  the  energy  of  the  rock  is  not  due  to  its  great  weight 
alone,  for  we  know  that  it  could  overcome  more  resistance  if 
it  were  moving  faster.  The  energy  of  the  bullet  is  not  due 
alone  to  its  great  velocity  ;  for,  let  a  heavier  ball  fly  with  the 
same  speed,  and  it  would  be  still  more  destructive. 


NATURAL  FHILOSOMY.  119 

In  these  cases  alike  the  energy  depends  on  both  mass  and 
velocity.  It  depends  on  nothing  else ;  and  its  relation  to 
these  two  things  is  stated  in  the  following 

Law.  —  The  energy  of  a  moving  body  is  proportional  to 
its  mass  and  to  the  square  of  its  velocity. 

A  simple  illustration  may  help  us  to  see  the  truth  of  this 
law.  Let  a  five-pound  ball  be  thrown  upward,  starting  with 
a  velocity  of  96  feet.  That  ball  would  rise  to  a  height  of  144 

feet  (v  =  \/2  g  s,  .'.  s  =  ~—  =  -«j-  =144),    and  the  work 

done  in  lifting  it  so  high  would  be  5  x  144  =  720  foot- 
pounds. And,  if  it  were  a  ten-pound  ball,  the  work  would 
be  10  x  144  =  1,440  foot-pounds.  Thus  a  double  mass  has 
the  ability  to  do  twice  as  much  work. 

Or  let  the  five-pound  ball  be  started  with  a  velocity  twice 
as  great,  192  feet.  Now,  this  velocity  will  carry  the  ball  to  a 
height  of  576  feet,  and  the  work  done  in  lifting  it  so  high 
is  5  x  576  =  2,880  foot-pounds  ;  and  this  is  four  times  as 
much  as  when  the  same  ball  started  with  a  velocity  of  96. 
Thus  a  double  velocity  gives  the  ability  to  do  four  times 
the  work.  In  the  same  way  three  times  the  velocity  would 
impart  nine  times  as  much  energy  to  the  moving  body. 

Relation  of  Energy  to  Work.  —  We  have  seen  that  the 
time  in  which  any  work  is  done  is  not  taken  into  account  in 
estimating  work.  To  place  a  ton  of  merchandise  upon  a 
freight-ca^',  the  same  amount  of  work  is  done,  whether  it  is 
done  in  one  hour  or  in  two  hours.  But  they  who  have  done 
it  in  one  hour  are  more  fatigued  than  if  they  had  spent  two 
hours  instead.  To  do  work  fast,  requires  more  energy  than 
to  do  it  slowly.  Time  is  thus  seen  to  be  an  element  in  com- 
puting energy. 

Comparison  of  Units.  —  The  relation  of  energy  to  work 
may  be  seen  again  by  comparing  their  units.  The  unit  of 
work  is  the  amount  of  work  done  in  lifting  a  one-pound  weight 
one  foot  high.  The  unit  of  energy  is  the  energy  expended 
in  lifting  a  one-pound  weight  one  foot  high  in  one  second. 


120  NATURAL   PHILOSOPHY. 

To  compute  Energy.  —  In  the  formula  v  =  \/2gs,  s  is 
the  height  to  which  a  body  will  rise  if  it  start  with  a  velocity 
represented  by  v.  If  you  transform  it  a  little,  }~ou  will  get 

v- 
s  =  — .     If,  then,  }'ou  know  the  velocity  of  a  body,  you  can 

easily  find  how  high  that  velocit}7  would  carry  it  if  it  were 
going  vertically  upward.  You  may  square  the  velocity,  and 
then  divide  by  the  value  of  2  g,  which  is  64^.  For  example  : 
An  arrow  is  shot  horizontally  with  a  velocity  of  96  feet  a 
second :  how  high  would  it  have  been  able  to  rise,  had  it 
been  shot  directly  upward?  96  X  96  =  9,216,  and  9,216-7- 
64^  =  143+ feet.  The  energy  of  the  arrow  would  be  able 
to  cany  it  143+  feet  high,  and  no  more. 

But  if  we  can  find  the  height  to  which  a  certain  velocity 
will  enable  a  body  to  rise,  we  can  quickly  find  the  work  which 
it  is  able  to  do  ;  for  we  need  only  multiply  the  weight  by  the 
height  to  find  it  in  foot-pounds. 

We  see,  then,  that,  in  order  to  find  how  much  work  a  mov- 
ing body  is  able  to  do,  we  must  multiply  its  weight  by  the 
square  of  its  velocity,  and  divide  the  product  by  64^. 

49.  Energy  is  of  two  types,  Kinetic  and  Potential. 
Kinetic  energy  is  the  energy  of  a  body  due  to  its  motion. 
Potential  energy  is  the  energy  of  a  body  due   to   some 
advantageous  position  it  holds.     (A.  183-189.) 

Kinetic  Energy.  —  The  arrow  while  at  rest  in  the  bow 
of  the  archer  has  no  power  to  overcome  resistance :  it  is 
without  energ}r.  In  its  flight  from  the  bow,  however,  it  has 
power  to  overcome  the  resistance  of  the  air,  and  to  pierce  the 
target.  The  energy  which  it  displays  is  due  to  its  motion, 
and  is  called  KINETIC  ENERGY. 

A  body  may  have  energjT  even  when  it  is  not  doing  work, 
as  a  man  may  possess  money  which  he  is  not  spending. 
If  a  body  were  falling  in  a  perfect  vacuum,  it  would  meet  no 
resistance,  and  hence  could  do  no  work.  Still  it  would  have 
the  power  to  do  work,  and  this  is  energy. 


NATURAL  PHILOSOPHY.  121 

Potential  Energy.  —  Again,  a  block  of  iron  resting  upon 
a  high  platform  has  power  to  overcome  resistances.  True, 
the  platform  prevents  the  exercise  of  that  power,  but  the 
power  is  in  it.  Take  away  this  hinderance,  and  the  block 
falls,  and  when  in  motion  expends  the  energy  which  was 
locked  within  it  while  at  rest.  The  energy  of  the  block  upon 
the  platform  is  due  to  its  position,  and  is  called  POTENTIAL 
ENERGY. 

The  Advantageous  Position.  —  The  block  resting  upon 
the  earth  has  no  energy  at  all ;  lift  it  to  the  platform,  and  it 
is  at  once  gifted  with  potential  energy.  The  high  position  is 
the  position  of  advantage.  The  block  must  be  placed  at 
a  distance  from  the  earth  in  order  to  be  endowed  with  poten- 
tial energy. 

Another  Definition.  —  Potential  energy  is  energy  due  to 
the  separation  of  two  bodies  which  are  acted  upon  by  a  force 
tending  to  bring  them  together. 

50.  There  are  several  varieties  of  energy.  When  dis- 
played in  masses  of  matter  it  is  called  Mechanical  Energy  ; 
in  molecules  it  is  called  Molecular  Energy ;  in  atoms  it  is 
Atomic  or  Chemical  Energy ;  in  undulations,  it  is  Radiant 
Energy ;  and  in  electrical  actions  it  is  Electrical  Energy. 
All  phenomena  are  only  different  exhibitions  of  these  varie- 
ties of  energy. 

Mechanical  Energy.  —  The  energy  of  the  train  swiftly 
gliding  along  its  iron  track,  of  the  waterfall  and  the  tornado, 
are  examples  of  energy  displayed  by  masses,  solid,  liquid, 
and  gaseous.  A  little  thought  will  suggest  many  others. 

Molecular  Energy.  —  But,  besides  this  energy  of  visible 
motion,  there  is  energy  of  invisible  molecular  motion.  We 
have  reason  to  believe  that  heat  is  the  energ}r  of  the  molecules 
swiftly  moving  among  themselves  while  the  body  itself  is  at 
rest. 

It  is  well  known,  for  example,  that  a  nail,  lying  upon  an 
anvil,  may  be  heated  until  it  can  burn  the  fingers,  by  simply 


122  NATURAL  PHILOSOPHY. 

pounding  it  with  a  hammer.  Now  we  suppose  that  the 
molecules  of  the  nail  tremble  under  the  blows  more  and 
more  as  the}T  are  repeated,  and  that  the  heat  we  feel  is  the 
energ}'  of  this  molecular  motion  spent  against  the  hand. 

Chemical  Energy.  —  Not  only  masses  and  molecules, 
but  atoms  also,  exhibit  energ}'.  Between  the  atoms  of 
oxygen  in  the  air  and  the  atoms  of  carbon  in  coal,  for 
example,  there  is  a  strong  attraction.  In  the  cold,  this 
attraction  can  not  bring  the  separate  atoms  together.  They 
are  in  a  condition  like  that  of  the  earth  and  the  block  of 
iron  which  is  kept  from  falling ;  their  energ}'  is  potential. 
But  if  the  atoms  of  ox}Tgen  and  carbon  can  be  allowed  to 
fall  together,  as  the  block  falls  to  earth,  their  energ}T  becomes 
kinetic.  This  is  what  happens  when  coal  burns  in  our  fur- 
naces or  elsewhere. 

Whatever  power  is  obtained  from  fire  is  primarily  due 
to  the  motion  of  atoms.  It  is  the  chemical  energy  in  the 
fuel  that  drives  the  engine  of  the  locomotive,  the  steamship, 
or  the  manufactory. 

Radiant  Energy.  —  When  a  cord  vibrates,  its  energy  is 
gradually  taken  away  by  the  air  until  finally,  when  all  is 
exhausted,  the  vibrations  cease. 

When  a  bell  is  struck,  its  molecules  vibrate,  but  their 
energy  is  gradually  given  up  to  the  air  until  exhausted,  when 
the  vibration  ends. 

B}T  these  and  all  other  vibraton-  motions,  the  air  is  thrown 
into  undulations  ;  and  this  undulatoiy  motion  of  the  air  pos- 
sesses all  the  energy  which  was  taken  from  the  cord  or  the 
bell  or  an}T  other  vibrating  bod}'. 

The  energy  exhibited  by  undulatoiy  motion,  in  whatever 
medium  it  exists,  is  called  radiant  energy,  because  the  undu- 
lations pass  awa}T  from  their  source  in  all  directions.  They 
radiate.  Radiant  energy  is  that  which  is  transmitted  b}' 
undulations,  outward  in  all  directions  from  a  center. 

Electrical  Energy.  —  The  power  of  electricity  to  over- 
come resistance  is  shown  in  every  thunder-shower.  The 


NATUKAL   PHILOSOPHY.  123 

lightning-flash  is  electricity  in  action,  tearing  a  pathway 
through  the  air  which  resists  its  passage.  And  trees  seen 
here  and  there,  which  have  been  torn  and  twisted  by  the 
lightning-stroke,  display  the  terrible  intensity  of  electrical 
energy. 


SECTION   II. 
ON  THE  CONSERVATION  OF  ENERGY. 

51.  Energy,  like  matter,  is  indestructible.  It  may  be 
transmitted  from  one  body  to  another ;  it  may  be  changed 
from  one  variety  into  another ;  but  the  sum  total  of  energy 
can  neither  be  increased  nor  diminished.  This  principle  is 
known  as  the  law  of  Conservation  of  Energy.  (G.  65,  66, 
484;  A.  190-193.) 

Energy  may  be  transmitted.  —  In  rolling  marbles,  when 
one  strikes  another  it  stops,  and  the  other  bounds  away. 
The  energ}T  passes  from  one  into  the  other.  Place  three  or 
four  in  a  row  against  the  edge  of  a  "  ruler  ' '  to  keep  them 
in  line,  and  then  roll  another  violently  against  the  end  of 
the  series.  The  ball  at  the  other  end  bounds  off,  while  the 
others  remain  at  rest.  The  energy  of  the  one  you  throw  is 
transmitted  from  ball  to  ball  until  it  reaches  the  last,  which 
keeps  it  all,  except  what  it  gives  up  to  the  air  and  the  table, 
which  resist  its  motion. 

Whenever  a  body  in  motion  meets  an  obstacle,  energy  is 
transmitted  to  it. 

Energy  may  be  transmuted.  — Let  a  ball  be  shot  ver- 
tically upwards  :  on  starting,  its  energy  is  kinetic.  But  it 
rises  more  and  more  slowly  until  it  stops,  and  then  falls 
again  to  the  ground.  Now,  at  the  moment  it  stops  at  the 
top  of  its  path,  its  energy  is  potential.  During  its  flight 
upward,  kinetic  energy  changes  into  potential  energy ;  and 
again,  during  its  fall,  potential  energy  is  changed  into  kinetic 


124  NATURAL  PHILOSOPHY. 

energy.  There  is  no  loss,  but  simply  a  change  in  the  char- 
acter of  the  energy. 

Observe  a  swinging  pendulum,  and  notice  a  similar  trans- 
mutation of  kinetic  and  potential  energy. 

Or  take  the  case  of  the  nail  which  is  warmed  by  the  blows 
of  a  hammer.  The  mechanical  energy  of  the  hammer  is  not 
lost  when  the  hammer  stops  :  it  has  been  changed  into  molecu- 
lar energy,  or  heat. 

Whenever  energy  disappears,  it  has  been  transmuted  into 
another  form. 

In  the  Exchange  110  Loss  occurs The  motion  of  a 

sledge-hammer  can  give  rise  to  a  certain  amount  of  motion 
among  the  molecules  of  the  anvil  on  which  it  falls, — no 
more,  no  less.  The  energy  of  the  hammer  is  changed  into 
molecular  energy :  it  appears  as  heat.  Now,  if  this  heat 
could  be  all  collected,  and  changed  back  into  mechanical 
energ}',  it  would  be  just  sufficient  to  lift  the  hammer  to  the 
height  from  which  it  fell.  The  amount  of  heat  produced  by 
a  given  energy  will  always  be  the  same,  and  when  it  dis- 
appears it  can  exert  an  energ}T  just  equal  to  that  which  caused 
it.  Nature  permits  no  loss  in  her  exchanges. 

The  mechanical  Equivalent  of  Heat.  —  Is  it,  then,  pos- 
sible to  tell  just  how  much  heat  will  be  produced  by  a  given 
amount  of  mechanical  energy,  or  how  much  energy  a  given 
amount  of  heat  may  exert?  This  has  been  done  with  the 
greatest  accuracy. 

The  first  Step  in  the  investigation  was,  to  settle  upon 
some  unit  by  which  to  measure  the  energy  exerted,  and 
another  by  which  to  measure  the  heat  produced.  The  unit 
of  energy  chosen  is  the  energy  exerted  by  a  weight  of  one 
pound,  falling  a  distance  of  one  foot.  The  unit  of  heat  is 
the  amount  of  heat  required  to  raise  the  temperature  of  one 
pound  of  water  1°  F. 

Next,  the  question  is,  how  many  units  of  mechanical 
energy  will  produce  one  unit  of  heat?  The  honor  of  first 
answering  this  question  is  shared  by  Dr.  Mayer  of  Germany, 


NATURAL   PHILOSOPHY.  125 

and  Mr.  Joule  of  England,  who,  at  about  the  same  time  and 
by  different  methods,  obtained  results  so  much  alike  as  to 
give  impartial  judges  great  confidence  in,  not  less  than 
admiration  of,  the  labors  of  both.  The  experiments  of 
Joule  extended  through  seven  laborious  years.  Dr.  Tyndall 
describes  them  fully  in  his  "Heat  as  a  Mode  of  Motion." 
This  author  goes  on  to  say,  "  It  was  found  that  the  quan- 
tity of  heat  which  would  raise  one  pound  of  water  one  degree 
Fahrenheit  in  temperature  is  exactly  equal  to  what  would 
be  generated  if  a  pound  weight,  after  having  fallen  through 
a  height  of  772  feet,  should  have  its  moving  force  destroyed 
by  collision  with  the  earth.  Conversely,  the  amount  of  heat 
necessary  to  raise  a  pound  of  water  one  degree  in  tempera- 
ture would,  if  all  applied  mechanically,  be  competent  to  raise 
a  pound  weight  772  feet  high,  or  it  would  raise  772  pounds 
one  foot  high.  The  term  '  foot-pound  '  has  been  introduced 
to  express  the  lifting  of  one  pound  to  the  height  of  a  foot." 
Then,  772  foot-pounds  is  what  is  called  the  MECHANICAL 
EQUIVALENT  OF  HEAT. 

The  three  Essentials  in  the  Law  of  Conservation.— 
The  three  characteristics  of  physical  energy  are  :  — 

1st,  It  may  be  transmitted.  —  If  one  body  gains,  another 
loses. 

2d,  It  may  be  transmuted.  —  If  one  form  disappears, 
another  takes  its  place. 

3d,  These  changes  are  mathematical.  —  The  quantity  is 
unchanged. 

The  Law  has  not  been  successfully  applied  to  social 
or  mental  Powers.  —  Work  of  the  most  exalted  kind  is 
wrought  by  the  action  of  mental  and  social  forces,  but  the 
law  of  conservation  has  not  yet  been  extended  over  these 
energies.  The  mind  which  acts  retains  its  mental  energy 
without  loss  :  there  seems  to  be  no  transmission.  It  retains 
it  the  same  in  kind :  no  transmutation  has  been  discovered. 
Moreover,  in  the  present  state  of  science  no  unit  of  measure 
for  mental  energy  can  be  suggested. 


126  NATURAL  PHILOSOPHY. 

SECTION  III. 

ON  THE  RECOGNITION  OF  ENERGY  BY  THE  SENSES. 

52.  Molecular  and  radiant  energy  affects  the  organs  of 
sense.  Acting  upon  the  sense  of  touch,  it  is  recognized  as 
Heat.  Transmitted  to  the  ear,  it  is  recognized  as  Sound. 
By  the  eye  it  is  recognized  as  Light.  (G.  284,  417,  485.) 

L— HEAT. 

Mechanical  Action  evolves  Heat.  —  When  the  sav- 
age lights  his  fire  by  rubbing  two  pieces  of  hard  wood  to- 
gether, he  produces  heat  \>y  friction.  When,  by  repeated 
blows  of  a  hammer,  a  nail  is  made  too  hot  to  handle,  or 
when  the  iron-clad  hoof  of  a  horse  "  strikes  fire  "  against  a 
pavement-stone,  heat  is  evolved  b}^  percussion.  And,  finally, 
when  a  piece  of  cold  wood  is  heated  by  being  squeezed  be- 
tween the  plates  of  a  hydrostatic  press,  heat  is  evolved  by 
pressure.  No  two  bodies  can  act  upon  each  other,  either  by 
friction,  by  blows,  or  by  sudden  pressure,  without  evolving 
heat. 

The  Dynamic  Theory.  —  It  is  now  generally  believed 
that  heat  is  a  kind  of  vibration,  whose  energy  can  affect  the 
sense  of  touch.  This  theory  supposes  matter  to  be  made 
up  of  molecules  separated  by  definite  distances  ;  it  goes  fur- 
ther and  supposes  these  molecules  to  be  in  motion,  rapidly 
vibrating  in  the  minute  spaces  between  them.  To  increase 
this  molecular  motion,  is  to  make  a  body  hot ;  to  lessen  it,  is 
to  make  the  body  cold.  The  theory  assumes  also  the  exist- 
ence of  the  ether,  which,  according  to  the  theory  of  light, 
must  fill  all  space. 

When  we  step  from  the  shade  into  the  sunlight,  the  gentle 
heat  of  its  rays  is  instantty  felt.  The  explanation  is  this : 
The  molecules  of  the  sun  itself  are  in  rapid  vibration  ;  they 
impart  motion  to  the  ether,  whose  undulations  dart  through 


NATURAL   PHILOSOPHY.  127 

the  space  between  the  sun  and  us,  and,  coming  in  contact 
with  the  person,  impart  their  energy  to  the  organ  of  the  sense 
of  touch,  when  we  become  immediately  conscious  of  the 
presence  of  heat. 

When  bodies  are  heated  by  friction,  their  molecules  are 
made  to  vibrate  faster  by  the  rubbing.  Heat  is  evolved  by 
percussion,  because  a  blow  increases  the  motion  of  the 
already  trembling  particles  of  the  body  struck.  The  same 
effect  is  produced  by  pressure. 

II.  — SOUND. 

Hearing  produced  by  Vibrations.  —  Let  two  books  be 
clapped  together,  and  every  ear  in  the  room  receives  a  shock, 
to  which  the  name  of  "  sound  "  is  given.  The  molecules  of 
the  books  are  made  to  vibrate  by  the  blow,  and  these  vibra- 
tions, acting  upon  the  air  in  contact  writh  them,  produce  air- 
waves. These  air-waves,  traveling  outward  in  all  directions, 
finally  reach  the  ear ;  and  the  many  parts  of  this  organ, 
receiving  the  energy  of  these  undulations,  enable  the  mind 
to  recognize  the  peculiar  sensation  which  we  call  sound. 

When  we  listen  to  the  sound  of  a  church-bell,  we  may  in 
like  manner  imagine  the  molecules  of  the  bell  all  in  a  state 
of  tremulous  motion,  caused  by  the  blows  of  the  hammer. 
This  motion  causes  undulation  in  the  air  in  contact  with  the 
bell.  The  air-waves  thus  formed  travel  in  all  directions 
from  the  bell  until  they  impart  their  energy  to  the  ear. 

The  roar  of  a  cataract  is  the  result  of  vibrations  caused  by 
the  falling  water.  The  rolling  sound  of  thunder  is  the  effect 
of  vibrations  in  air,  caused  by  electricity.  Every  sound  in 
nature,  or  that  can  be  produced  by  art,  may  be  traced  back 
through  the  waves  of  some  medium,  to  the  vibrating  mole- 
cules of  a  solid,  liquid,  or  gaseous  body. 

Sound.  —  In  the  study  of  physics,  the  word  "  sound  "  re- 
fers to  the  undulations  outside,  rather  than  to  the  sensation 
in,  the  ear.  Sound  is  an  undulatory  motion  in  an  elastic 
medium  whose  energy  can  affect  the  ear. 


128  NATURAL   PHILOSOPHY. 


III. —LIGHT. 

Light  is  undulatory  Motion.  —  It  was  once  thought 
that  light  consists  of  minute  particles  of  matter  thrown  in 
great  abundance  from  the  sun  and  some  other  bodies.  It  is 
now  generally  believed  that  light  is  a  kind  of  undulation. 
But  light  will  pass  through  the  most  perfect  vacuum  that 
can  be  made.  Moreover,  the  atmosphere  extends  but  a  few 
miles  above  the  earth,  yet  the  light  from  the  sun  comes  in 
floods  through  the  vast  distance  which  separates  these  bodies  : 
what  can  there  be  between  the  sun  and  the  earth,  whose 
undulations  bring  to  us  the  energy  of  sunlight? 

The  Ether.  —  Philosophers  assume  that  there  is  a  thin, 
elastic  substance  called  ether,  much  finer  and  rarer  than  air, 
which  fills  all  the  spaces  between  the  heavenly  bodies,  and 
enters  into  all  those  between  the  molecules  of  matter  in 
every  form.  The  undulations  of  this  ether  pass  through  a 
vacuum,  through  celestial  spaces,  through  bodies  like  glass, 
and  through  the  substances  of  the  eye,  until  they  strike  the 
nerves  of  sight. 

Vision.  —  When  a  gas-jet  is  suddenty  lighted  in  a  dark 
room,  every  eye  present  is  dazzled  by  the  brightness  of  the 
light.  The  explanation  is  this :  The  heated  gas  makes  the 
ether  in  contact  with  it  vibrate.  This  ether  is  between 
the  particles  of  the  air,  and  between  the  molecules  of  the 
substance  of  the  eye.  Its  undulations,  starting  from  the  gas- 
jet,  go  through  the  air  and  into  the  eye  ;  and,  when  these 
undulations  of  the  ether  impart  their  energj-  to  the  delicate 
nerves  in  the  back  part  of  this  organ,  we  are  made  conscious 
of  the  presence  of  light. 

Luminous  Bodies.  —  Bodies  which  shine  by  their  own 
light  are  called  LUMINOUS  bodies.  They  are  bodies  which 
can  start  undulations  in  the  ether.  Bodies  which  shine  only 
by  light  which  they  receive  from  others  are  called  NON- 
LUMINOUS  bodies :  they  can  not  start  undulations  in  the 
ether.  The  sun  is  a  luminous  body :  so  is  a  red-hot  iron 


NATURAL   PHILOSOPHY.  129 

ball.  All  flames  are  luminous  bodies.  The  moon  is  non- 
luminous.  Almost  all  bodies  on  the  earth  are  non-luminous : 
the  light  which  they  give  to  us  is  light  which  the  sun  first 
gave  to  them. 

Light.  —  Light  is  the  undulation  of  the  ethereal  medium 
whose  energy  produces  vision. 

Manifestations  of  Energy.  —  All  the  phenomena  of  heat 
and  sound  and  light  can  be  best  explained  by  regarding  them 
as  only  so  many  different  exhibitions  of  molecular  and  radi- 
ant energy. 

SECTION   IV. 

REVIEW. 
I.  —  SUMMARY   OF  PRINCIPLES. 

Force  is  that  which  in  any  way  tends  to  affect  the  condi- 
tion of  a  body  as  to  rest  or  motion. 

Work  is  the  overcoming  of  resistance. 

Energy  is  the  ability  to  do  work. 

The  unit  of  force  is  the  force  needed  to  move  a  unit  of 
mass  at  the  rate  of  one  foot  a  second. 

The  unit  of  work  is  the  work  done  in  lifting  one  pound  to 
a  height  of  one  foot. 

The  unit  of  energy  is  the  energy  expended  in  lifting  one 
pound  a  foot  high  in  one  second. 

To  find  the  numerical  value  of  a  force,  multiply  the  mass 
which  the  force  moves,  by  the  velocity  with  which  it  is 
moved. 

This  product,  viz.,  mxv,  is  called  the  MOMENTUM  of  the 
body.  The  momentum  of  a  moving  bod}'  is  a  measure  of 
the  force  which  is  moving  it. 

To  find  the  work  done  in  lifting  a  bod}*,  multiply  the 
weight  of  the  body  by  the  vertical  height  to  which  it  is 
lifted. 

To  find  the  energy  in  a  moving  body,  multiply  the  weight 


130  NATURAL   PHILOSOPHY. 

of  the  body  by  the  square  of  its  velocity,   and  divide  by 


Kinetic  energy  is  the  ability  of  a  moving  body  to  over- 
come resistance. 

Potential  energy  is  the  ability  of  a  body  at  rest  when  in 
some  high  or  advantageous  position,  to  overcome  resistance- 

Energy  of  these  two  types  is  mechanical,  molecular,  chem- 
ical, radiant,  or  electrical,  taking  its  name  from  the  kind  of 
work  in  which  it  appears. 

All  physical  phenomena  are  only  different  exhibitions  of 
energy. 

PHYSICS  is  THE  SCIENCE  OF  MATTER  AND  ENERGY. 

II.—  SUMMARY    OF  TOPICS. 

45.  Mass  and  its  measure. 

46.  Force  and  its  measure. 

47.  Work.  —The   unit.—  The   French   unit.  —  Rule    for 
calculating  work.  —  Work  independent  of  time.  —  When  the 
body  is  not  lifted  verticall}-. 

48.  Energy  defined.  —  Energy  depends  on  mass  and  ve- 
locity. —  The   law.  —  Illustrated.  —  Relation    of    energy   to 
work.  —  Comparison  of  units.  —  To  compute  energy. 

49.  Kinetic  energy.  —  Potential   energ}".  —  The   advanta- 
geous position.  —  Another  definition  of  potential  energy. 

50.  Mechanical   energy*.  —  Molecular   energy.  —  Chemical 
energy.  —  Radiant  energ}'.  —  Electrical  energ}'. 

51.  Energy  may  be  transmitted.  —  Energy  may  be  trans- 
muted. —  No  loss  of  energy  in  the  changes.  —  The  mechan- 
ical equivalent  of  heat.  —  The  three  essentials  in  the  law  of 
conservation. 

52.  Mechanical  action  evolves  heat.  —  The  dynamic  theo- 
ry. —  Hearing  produced  by  vibrations.  —  Sound.  —  Light  is 
undulatoiy     motion.  —  The     ether.  —  Vision.  —  Luminous 
bodies.  —  Light  defined.  —  Manifestations  of  energy. 


NATURAL  PHILOSOPHY.  131 


III.  —  PROBLEMS. 

1 .  What  FORCE  is  required  to  put  a  ball  of  iron  weighing 
one  pound  in  motion,  with  a  velocity  of  one  foot  a  second? 

Ans.  1  unit. 

2.  What  is  the  MOMENTUM  of  one  pound  moving  with  a 
velocity  of  one  foot  a  second?  Ans.  1  unit. 

3.  A  locomotive  weighing  ten  tons  is  to  be  put  in  motion 
with  a  velocity  of  thirty  feet  a  second  :  what  FORCE  must  the 
steam  exert?  Ans.  600000  units. 

4.  What  is  the  MOMENTUM  of  a  ball  weighing  ten  pounds, 
and  flying  with  a  velocity  of  seventy-five  feet  a  second  ? 

Ans.  750  units. 

5.  How  much  WORK  must  be  done  to  lift  a  bucket  filled 
with  water,  weighing  twenty  pounds,  from  the  bottom  to  the 
top  of  a  well  which  is  fifteen  feet  deep  ? 

Ans.  300  foot-pounds. 

6.  A  person  whose  weight  is  120  pounds  ascends  a  flight 
of  stairs,  reaching  between  two  floors,   which  are   12  feet 
apart :  how  much  WORK  does  he  do  ? 

Ans.  1440  foot-pounds. 

7.  Find  the  ENERGY  of  a  body  weighing  five  pounds,  and 
moving  at  the  rate  of  45  feet  a  second. 

Ans.  157.38-j-  foot-pounds. 

8.  What  is  the  ENERGY  of  a  locomotive  whose  weight  is 
ten  tons,  and  which  is  moving  at  the  rate  of  thirty  miles  an 
hour?  Ans.  601865.28+  foot-pounds. 

9.  Suppose  the  locomotive  whose  energy  is  found  in  the 
preceding   problem   should   meet   another  having  the  same 
weight  and  velocity,  what  amount  of  energy  would  be  ex- 
pended to  dash  them  to  pieces? 

Ans.  1203730.56  foot-pounds. 

10.  Suppose  it  were  possible  to  convert  the  energy  of  the 
collision  of  these  two  locomotives  into  heat,  how  much  water 
would  the  heat  produced  be  able  to  raise  from  32°  F.  to 
212°  F.?  Ans.  8.66+  pounds. 


132  NATURAL  PHILOSOPHY. 


CHAPTER  V. 
ON  MOLECULAR  ENERGY:    HEAT. 


SECTION   I. 
ON  CONDUCTION  AND  CONVECTION. 

53.  HEAT  is  conducted  through  some  bodies  much  more 
freely  than  through  others.  Among  solids  the  metals  are 
the  best  conductors.  Liquids  are  poor  conductors,  and 
gases  still  poorer.  (G.  392,  394-398  ;  A.  601,  602.) 

Conduction.  —  Suppose  that  one  end  of  a  cold  iron  rod 
is  held  in  the  flame  of  a  lamp.  The  heat  will  travel 
gradually  from  the  flame  through  the  rod,  until  the  distant 
end  becomes  too  warm  to  be  held  by  the  hand.  The  heat 
travels  step  by  step  from  molecule  to  molecule  to  the  end. 
This  mode  of  transmitting  heat  is  called  CONDUCTION. 

Explanation.  — :  If  we  would  understand  how  the  heat 
has  made  its  little  journey  through  the  rod,  we  must  picture 
to  ourselves  the  delicate  motion  of  the  molecules  of  the 
iron.  Those  molecules  in  contact  with  the  flame  are  made 
to  vibrate ;  the}T  swing  against  their  neighbors,  and  put 
them  also  in  more  rapid  motion ;  they,  in  turn,  give  motion 
to  the  next,  and  these  to  the  next,  until  those  at  the  distant 
end  of  the  rod  have  finally  received  the  shock.  The  energy 
of  these  molecules  of  the  rod  is  intercepted  b}r  the  hand 
in  contact  with  them ;  the  delicate  nerves  of  touch  receive 
the  impulses,  and  announce  the  pain. 

Definitions.  —  Some  bodies  conduct  heat  more  freely 
than  others.  Those  which  conduct  heat  freely  are  called 


NATURAL   PHILOSOPHY. 


133 


CONDUCTORS  ;  those  which  hinder  its  passage  much  are 
called  POOR  CONDUCTORS  ;  and  those  which  nearly  or  quite 
forbid  its  passage  are  called  NON-CONDUCTORS.  The  prop- 
ert^y  in  virtue  of  which  bodies  conduct  heat  is  called  CON- 
DUCTIVITY. 

Metals  are  good  Conductors.  —  Among  solid  bodies 
the  metals,  as  a  class,  are  the  best  conductors,  but  among 
metals  there  is  great  difference  in  conducting  power.  By  a 
very  simple  experiment  this  may  be  illustrated.  Plunge  two 
spoons,  one  of  silver  and  the  other  of  German  silver,  into 
the  same  cup  of  hot  tea :  it  will  be  found  that  the  upper  end 
of  the  silver  spoon  will  become  hot  much  quicker  than  that  of 
the  other.  Among  the  best  conductors  we  find  silver,  cop- 
per, gold,  brass,  tin,  and  iron,  in  the  order  named. 

The  Conductivity 
of  Liquids. — The  con- 
ducting power  of  liq- 
u i d s  is  very  feeble. 
Wa  t  e  r ,  for  example , 
in  a  glass  tube,  with  ice 
at  the  bottom,  may  be 
boiled  without  melting 
the  ice,  by  applying  the 
heat  to  the  top  of  the 
water,  or  near  the  upper 
end  of  the  tube.  (Fig. 
60.) 

The  Conductivity 
of  Gases.  —  Whether 
gases  conduct  heat  in  the 
least  degree,  is  doubted. 
Dry  air  is  surely  among 
the  poorest  conductors ; 
and  so,  likewise,  are  all 


Fig.  60. 


porous  substances  in  which  large  quantities  of  air  are  in- 
closed. 


134  KATtJ&AL  PHILOSOPHY. 

54.  Convection  takes  place  in  bodies  whose  particles  arc 
free  to  move.  Air  is  heated  in  no  other  way.  Liquids  are 
also  heated  by  convection :  solids  never  are. 

Convection.  —  Heat  is  transmitted  by  convection  when 
it  is  carried  from  place  to  place  by  moving  particles  of 
matter.  The  following  very  simple  experiment  will  make 
this  definition  clear.  Upon  a  plate  of  thick  glass  or  a  smooth 
block  of  wood  put  a  bit  of  candle,  lighted,  and  over  it  place 
a  lamp-chimney  so  that  its  edge  may  project  a  little  be}rond 
the  edge  of  the  block  (Fig.  61).  If  the  edge  of  the  chimney 
fits  closely  upon  the  top  of  the  block,  so  that  no  air  can  enter 
except  at  the  open  part  A,  the  flame  will  flut- 
ter violently,  showing  that  air  is  forced  against 
it.  If  some  light  substance,  such  as  down  or 
cotton,  be  hung  from  a  thread  above  the  top 
of  the  chimney,  it  will  be  lifted  away,  showing 
that  air  is  rising  out  of  the  chimney.  Now,  we 
lg'  '  know  alread}'  that  air  is  expanded  by  the  heat ; 
and  we  learn  from  this  experiment  that  the  cold  air  going 
under  the  glass  pushes  the  expanded  air  away  from  the  flame, 
up  and  out  at  the  top  of  the  chimne}*. 

What  we  have  seen  in  this  experiment  really  takes  place 
whenever  a  hot  body  is  surrounded  by  colder  air.  The  air 
in  contact  with  a  hot  stove,  for  example,  is  heated  and  ex- 
panded. The  colder  air  then  pushes  it  away,  and  takes  its 
place,  only  in  turn  to  be  heated  and  pushed  away  by  other 
colder  portions.  The  air  goes  to  the  stove,  becomes  heated, 
and  moves  away  to  other  parts  of  the  room,  carrying  the  heat 
with  it.  This  transfer  of  heat  by  the  moving  particles  is  called 
CONVECTION. 

Air  is  heated  in  no  other  Way.  —  Air  is  heated  only 
by  convection.  The  heat  of  a  stove  does  not  go  out  to  dis- 
tant parts  of  a  room  to  warm  the  air :  the  air  must  go  to  the 
stove  to  be  warmed.  So,  too,  the  atmosphere  is  warmed  by 
convection.  The  sunbeams  coming  through  it  do  not  warm 


KATUBAL   PHILOSOPHY.  135 

it :  they  only  warm  the  earth  beneath  it.  Nor  does  the  heat 
of  the  earth  pass  from  particle  to  particle  of  the  air,  as  it 
may  in  solid  bodies  :  the  heat  of  the  earth  warms  only  those 
particles  in  immediate  contact  with  it.  These  rise  and  carry 
their  heat  with  them  to  upper  regions,  while  colder  ones  take 
their  places  in  contact  with  the  ground  to  get  warm  in  turn, 
and  then  ascend. 

liquids  heated  by  Convection.  —  Liquids  are  also  heat- 
ed  by  convection.  A  simple  experiment  will  illustrate  the 
convection  of  water.  Into  a  flask  or  bottle  of  water  put 
a  little  cochineal.  Its  particles  are  just  about  as  heavy  as 
those  of  the  water,  and  will  show  by  their  motion  whether 
there  are  current^  in  the  water.  Warm  the  bottom  of  the 
bottle,  and  the  heated  water  will  be  seen  to  be  rapidly  leav- 
ing the  bottom,  while  other  portions  are  moving  downward 
to  take  its  place. 

No  Convection  in  Solids.  —  Solids  can  not  be  heated  by 
convection,  simpl}7  because  their  particles  are  not  free  to 
move  among  themselves. 

SECTION  II. 

ON  THE  EFFECTS  OF  HEAT. 

55.  The  action  of  heat  is  twofold  :  it  raises  the  tempera- 
ture of  a  body  to  which  it  is  applied,  and  at  the  same  time 
expands  it.  This  is  true  of  its  action  upon  Solid,  Liquid, 
and  Gaseous  bodies.  (G-.  303,  304,  309,  310  ;  A.  660.) 

The  Action  of  Heat  is  Twofold.  —  That  the  temper- 
ature of  bodies  is  raised  by  the  application  of  heat,  is  too 
familiar  to  need  illustration.  That,  while  the  temperature 
rises,  the  body  grows  larger,  is  known  by  such  facts  as  the 
following:  A  ball  of  metal,  which,  when  cold,  just  fits  a 
ring,  will  be  too  large  to  enter  it  when  hot.  A  clock-pendu- 
lum is  longer  in  summer  than  in  winter.  The  tire  of  a 
carriage-wheel  is  put  on  while  hot ;  on  cooling,  it  contracts, 
and  binds  the  parts  of  the  wheel  firmly  together. 


136  NATURAL   PHILOSOPHY. 

The  Expansion  of  Solids.  —  The  expansion  of  a  solid  b}' 
heat  may  be  shown  by  an  experiment.  A  ball  of  iron  or  of 
brass  is  taken,  just  large  enough  to  pass  easily  through  a  ring 
of  the  same  material.  The  ball  is  then  heated  by  a  lamp, 
after  which  it  will  be  too  large  to  go  through  the  ring.  It 
will  rest  upon  the  ring  (Fig.  62)  until  it  is  cold  again, 
when  it  once  more  passes  easily  as  at  first.  We  see  that 
heat  makes  this  ball  larger.  And  it  has  the  same  effect  upon 
other  solids. 

Different  solids  expand  unequally  for  the  same  increase  of 
temperature  ;  but  each  solid  expands  uniformly,  —  that  is  to 
say,  two,  three,  or  ten  degrees  of  heat  will  produce  respec- 


Fig.  62. 

tivety  two,  three,  or  ten  times  as  much  expansion  as  one 
degree. 

Expansion  of  Liquids.  —  To  show  the  expansion  of  a 
liquid  a  glass  bulb  with  a  long  open  stem  is  used.  The  bulb 
is  filled  with  water,  and  the  stem  partty  filled,  after  which,  if 
the  bulb  is  plunged  into  hot  water  (Fig.  63),  the  water  in 
the  stem  will  be  seen  slowly  rising. 

Illustrations.  —  A  kettle  very  nearly  full  of  cold  water 
will  be  quite  full  when  the  water  is  heated  :  the  water  will  run 
over  long  before  it  boils. 

Twenty  gallons  of  alcohol  in  midwinter  will  become  about 
twenty-one  gallons  in  midsummer. 


NATURAL   PHILOSOPHY. 


137 


The  Expansion  of  Gases.  —  The  expansion  of  gases 
is  more  nearly  uniform  than  that  of  either  solids  or  liquids, 

and  much  greater  for  the 
same  addition  of  heat. 
What  is  more  remarkable 
is  the  fact  that  they  all 
expand  at  the  same  rate. 
If  we  have  491  cubic 
inches  of  air  at  a  tem- 
perature of  32°  F.,  and 
add  one  degree  of  heat, 
there  will  be  492  cubic 
inches  :  it  expands  ^y  of 
its  bulk.  All  gases  ex- 
pand at  the  same  rate, 
4^  of  their  bulk  at  32°, 
for  every  additional  de- 
gree. This  fraction  (^Jy) 
of  its  volume  at  32°  F., 
which  a  gas  expands  for 
every  degree  of  tempera- 
ture, is  called  the  CO- 
EFFICIENT OF  EXPANSION 
for  gases. 

56.  Temperature  is 
measured  by  the  expan- 
sion  which   accompanies 
Flg'  63'  it,  in  instruments  called 

thermometers.  There  are  three  varieties  of  thermometers 
in  use,  —  the  Fahrenheit,  the  Centigrade,  and  the  Reaumur. 
The  air-thermometer  is  used  to  show  delicate  changes  of 
temperature.  (G.  287-293.) 

Temperature  measured  by  Expansion.  —  We  have 
found  that  temperature  and  expansion  increase  at  the  same 
time  by  the  addition  of  heat.  Moreover,  in  the  same  body 


138  NATURAL   PHILOSOPHY. 

a  certain  amount  of  expansion  always  occurs  with  the  same 
increase  of  temperature.  By  seeing  the  expansion  we  may 
therefore  judge  of  the  increase  of  temperature. 

The  expansion  of  solids  is  too  slight,  while  that  of  gases 
is  too  great,  to  be  conveniently  used  to  measure  the  changing 
temperature  of  the  air  and  other  things.  Mercury  is  a  liquid 
metal,  whose  expansion  is  remarkably  uniform,  and  neither 
too  great  nor  too  little  for  practical  purposes.  All  common 
thermometers  are  made  with  it. 

The  Thermometer.  —  The  mercurial  thermometer  con- 
sists of  a  glass  tube  terminating  at  one  end  in  a  bull),  and 
sealed  at  the  other.  The  bulb  and  lower  part  of  the  tube 
are  filled  with  mercury,  the  space  in  the  tube  above  the 
mercury  being  a  vacuum.  Behind  the  tube  is  a  graduated 
scale  to  show  the  height  of  the  column  of  mercury. 

There  are  three  modes  of  graduating  the  scale,  and  this 
gives  rise  to  three  varieties  of  mercurial  thermometer. 

Fahrenheit.  —  In  the  Fahrenheit  thermometer,  the  zero 
of  the  scale  marks  the  height  of  the  mercury  in  the  tube  when 
the  bulb  is  placed  in  a  mixture  of  snow  and  salt.  When 
the  bulb  is  put  into  boiling  water,  the  mercury  in  the  tube 
runs  up  to  a  point  which  is  marked  212  on  the  scale.  The 
distance  between  these  points  is  divided  into  212  equal  parts 
called  degrees,  and  this  graduation  is  carried  above  and  below 
these  points.  According  to  this  thermometer,  water  boils  at 
212°,  and  freezes  at  32°. 

Centigrade.  —  In  the  centigrade  thermometer,  the  zero 
point  marks  the  height  of  the  mercury  in  the  tube  when  the 
bulb  is  placed  in  freezing  water.  The  height  to  which  it 
rises  when  the  bulb  is  put  into  boiling  water  is  marked  100, 
and  the  distance  between  these  points  is  divided  into  100 
equal  parts.  The  boiling  point  of  water  is,  therefore, 
100°  ;  its  freezing  point  is  0°. 

R&uimur. —  In  the  Reaumur  thermometer,  the  zero  marks 
the  freezing  point  of  water ;  the  boiling  point  is  marked  80. 

Below  Zero.  —  Degrees  of  temperature  below  the    zero 


NATURAL    PHILOSOPHY.  139 

point  are  generally  indicated  by  the  minus  sign  (  — )  placed 
before  the  number.  Thus,  —40°  means  a  temperature  40° 
below  zero. 

Otlior  Forms.  —  Mercury  freezes  at  about  —39°  F. 
Temperatures  below  this  point  are  measured  by  thermometers 
containing  alcohol.  Mercury  boils  at  660°  F  :  tern-  /"~"\ 
peratnres  above  this  point  are  measured  by  the  ex-  I  ) 
pansion  of  solid  bodies. 

When  it  is  necessary  to  show  very  delicate  changes 
of  temperature,  the  air-thermometer  .is  used.  This 
instrument  has  a  variety  of  forms,  but  it  consists 
essentially  of  a  glass  tube,  terminating  at  one  end 
in  a  bulb,  the  other  end  being  open,  and  inserted 
into  a  cistern  of  colored  liquid.  (See  Fig.  64.) 
The  liquid  fills  a  part  of  the  tube :  the  rest  of  the  HO 
tube  and  the  bulb  above  is  filled  with  air.  A  gradu- 
ated scale  is  placed  behind  the  tube.  The  air  ex- 
pands or  contracts  with  every  change  of  tempera- 
ture, and  accordingly  drives  the  colored  liquid  down,^ 
or  allows  it  to  rise  in  the  tube.  The  motion  of  the 
liquid  shows  the  change  in  the  temperature. 


57.  Temperature  is  the  manifestation  of  kinetic 
energy :  expansion,  of  potential.     The  first  affects 
the  touch,  and  is  called  SENSIBLE  HEAT.     The  sec- 
ond  does  not  affect  the  touch,  and  is  called  LATENT  J I  KAT. 
(G.  434,  435*  438,  439,  443  ;  A.  670.) 

Rapidity  of  Motion,  and  Change  of  Position.  —  He 

who  has  a  clear  idea  of  the  molecules  can  distinctly  imagine 
the  multitude  of  these  little  bodies  of  which  any  larger  body 
is  made  up,  separated  from  each  other  by  minute  distances 
and  in  rapid  motion.  Now,  heat  can  make  them  vibrate 
faster ;  it  may  also  push  them  farther  apart,  or  otherwise 
change  their  position  :  it  can  do  nothing  more.  Then,  when 
heat  is  being  applied  to  a  bar  of  iron,  let  the  mind  picture 
to  itself  these  two  effects :  the  molecules  of  the  bar  vibrating 


140  NATURAL   PHILOSOPHY. 

more  and  more  swiftly,  and  at  the  same  time  being  pushed 
farther  and  farther  apart.  The  first  of  these  effects  is  mani- 
fested as  temperature,  the  second  as  expansion. 

In  the  first  we  have  molecules  in  motion,  or  kinetic  energy. 
In  the  second  we  have  molecules  separated,  or  potential 
energ}7. 

Sensible  and  Latent  Heat.  —  The  heat  which  is  ex- 
pended in  raising  temperature  is  called  SENSIBLE  HEAT  :  it 
can  affect  the  sense  of  touch.  That  which  is  used  to  pro- 
duce expansion  or  change  the  positions  of  the  molecules  of 
a  body  is  called  LATENT  HEAT  :  it  does  not  affect  the  sense 
of  touch.  Now,  the  heat  that  goes  into,  or  acts  upon,  any- 
body, is  divided  into  these  two  portions ;  one  part  sensible, 
the  other  latent. 

Specific  Heat.  —  But  different  substances  do  not  divide 
it  alike ;  that  is,  if  the  same  amount  be  added  to  two  sub- 
stances, one  of  them  will  devote  more  of  it  to  temperature, 
and  less  to  expansion,  than  the  other. 

Let  equal  weights  of  water  and  mercuiy  be  placed  over 
the  same  source  of  heat.  The  water  divides  the  heat  it  re- 
ceives into  two  parts,  one  to  raise  its  temperature,  the  other 
to  expand  it.  The  mercury,  receiving  the  same  amount, 
divides  it  into  two  parts  devoted  to  the  same  purposes,  but 
the  heat  devoted  to  temperature  is  more  than  in  water,  while 
that  devoted  to  expansion  is  less.  We  find  that  the  tempera- 
ture of  mercury  rises  much  faster  than  that  of  water :  it  takes 
thirt}7  times  as  long  to  raise  the  water  to  a  given  temperature 
as  it  does  the  mercuiy.  If  it  take  thirty  times  as  long,  and 
one  receives  heat  as  fast  as  the  other,  there  must  be  thirty 
times  as  much  heat  in  the  water  as  in  the  mercuiy  when  that 
temperature  is  reached  by  both.  We  see,  then,  that  at  the 
same  temperature  different  substances  may  have  very  differ- 
ent quantities  of  heat  in  them.  The  relative  quantities  of 
heat  in  different  bodies,  at  the  same  temperature,  is  called 
SPECIFIC  HEATS. 

Water  is  the  Standard  of  Specific  Heat. — At  a  given 


NATURAL  PHILOSOPHY.  141 

temperature  water  contains  more  heat  than  any  other  known 
substance.  Its  specific  heat  being  1,  the  specific  heats  of  all 
other  substances  are  fractional.  The  specific  heat  of  mercury 
is  .03.  By  this  is  meant,  that,  when  equal  weights  of  mer- 
cury and  water  are  at  the  same  temperature,  the  mercury 
will  contain  only  .03  as  much  heat  as  the  water. 

58.  The  expansion  of  a  solid  body  will  continue  nearly 
uniform  until  its  temperature  has  reached  the  melting  point. 
The  temperature  then  stops  rising,  while  the  expansion  in- 
creases and  continues  until  the  solid  is  melted.  (6r.  327- 
329,  335,  336.) 

The  Melting1  Point.  —  The  temperature  at  which  a  solid 
body  begins  to  melt  is  called  its  MELTING  POINT.  At  this 
temperature,  the  repulsive  force  of  heat  nearly  balances  the 
cohesion  of  the  molecules,  and  enables  them  to  move  freely 
among  themselves.  The  body  becomes  a  liquid,  and  the 
change  from  the  solid  to  the  liquid  form  is  called  LIQUEFAC- 
TION. The  melting-point  for  different  substances  is  not  the 
same.  Ice  melts  at  32°  F.  ;  mercuiy  at  —.39° ;  iron  at 
about  3000°,  and  platinum  at  about  5000°. 

The  Temperature  stops  rising.  —  If  heat  be  applied  to 
a  vessel  of  ice  at  32°,  the  ice  will  melt,  and  the  water  formed 
will  have  the  same  temperature,  32°.  So,  too,  when  wax 
or  iron  or  lead  is  melted,  the  liquid  will  have  the  same  tem- 
perature as  the  solid  which  is  melting. 

But  the  Expansion  increases.  —  But  in  the  case  of  all 
the  substances  above  named,  except  ice,  the  expansion  is 
greater  at  the  melting  point  than  before  it  was  reached.  The 
liquid  fills  more  space  than  the  solid  from  which  it  was 
formed.  It  should  be  so,  because  the  heat  is  all  expended 
to  change  the  position  of  the  molecules,  whereas,  before,  a 
part  of  it  was  used  up  to  produce  a  rise  of  temperature. 

An  Exception.  —  Ice  contracts  when  melting  ;  the  water 
formed  fills  less  space  than  the  ice.  In  this  case,  likewise, 
all  the  heat  applied  is  expended  in  changing  the  position  of 


142  NATURAL  PHILOSOPHY. 

the  molecules,  but  not  in  pushing  them  farther  apart,  for 
they  occupy  less  space  than  before  the  change  occurred. 
The  change  consists  in  throwing  the  molecules  out  of  their 
crystalline  arrangement.  The  water  will  continue  to  contract 
until  it  reaches  a  temperature  of  39°,  after  which  it  expands. 
Those  who  have  attempted  to  melt  ice  or  snow,  for  domes- 
tic purposes,  remember  how  slow  the  process  is.  The  amount 
of  heat  required  to  simpty  melt  the  snow,  without  making  it 
any  warmer,  is  very  great ;  the  same  amount  applied  to  the 
water  formed  would  raise  its  temperature  142°.  This  is 
the  amount  of  heat  which  is  used  up  in  changing  the  relative 
positions  of  the  molecules,  and  becomes  latent.  Hence  the 
latent  heat  of  water  is  said  to  be  142°. 

59.  The  expansion  of  a  liquid  will  continue  gradual  until 
the  Boiling  Point  is  reached,  a  temperature  depending  upon 
the  Purity  of  the  liquid,  upon  the  Nature  of  the  vessel  in 
which  it  is  heated,  and  upon  the  Pressure  it  sustains.  At 
the  boiling  point,  the  temperature  stops  rising,  while  the  ex- 
pansion greatly  increases,  and  continues  until  the  liquid  is 
vaporized.  (G.  351,  352,  354,  358  ;  A.  684.) 

The  Boiling  Point.  —  The  temperature  at  which  a  liquid 
begins  to  boil  is  called  its  BOILING  POINT.  At  this  tempera- 
ture, the  body  rapidly  becomes  a  vapor,  and  the  change  is 
called  VAPORIZATION. 

Evaporation.  —  Liquids  do  indeed  change  to  vapor  at  all 
temperatures.  Even  from  freezing  water,  more  or  less  vapor 
is  ever  slowly  rising.  This  slow  change  is  called  EVAPORA- 
TION. The  boiling  point  for  different  liquids  is  not  the  same. 
Water  boils  at  212°  F.,  alcohol  at  173°,  ether  at  95°.  The 
boiling  point  for  the  same  liquid  is  not  always  the  same :  it 
depends  upon  three  circumstances. 

The  Boiling  Point  depends  on  the  Purity  of  the 
Liquid.  —  It  is  affected,  first,  b}r  the  presence  of  impurities 
in  the  liquid.  The  presence  of  some  impurities  raises  the 
boiling  point ;  of  others,  lowers  it.  Salt  water,  for  example, 


NATURAL  PHILOSOPHY. 


143 


boils  at  a  higher  temperature  than  pure  water,  while  that 
which  contains  air  boils  at  a  much  lower  temperature  than 
that  which  contains  none. 

It  depends  on  the  Nature  of  the  Vessel.  —  In  an  iron 
vessel,  water  will  boil  at  a  lower  temperature  than  in  one  of 
glass.  It  is  so  because  there  is  a  stronger  adhesion  between 
water  and  glass  than  between  water  and  iron.  The  stronger 
adhesion  requires  a  stronger  heat  to  overcome  it. 

It  depends  on  the  Pressure.  —  But  the  most  impor- 
tant circumstance  on  which  the  boiling  point  of  a  liquid 
depends  is  the  pressure  it  sustains.  This  pressure  is  due 
to  the  atmosphere,  to  the  weight  of  the  liquid  itself,  and  to 
any  force  which  may  be  brought  to  bear  upon  it  by  artificial 
means.  Whatever  ma}^  be  its  cause,  the  effect  of  pressure  is 
to  raise  the  boiling  point.  It  is  well  known  that  water  boils 
at  a  lower  temperature  on  the  top  of  a  mountain  than  at  its 
base.  It  does  so  because  the  pressure  of  the  air  upon  it  is  less. 

This  very  important  principle  may  be  easily  illustrated  by 
experiment.  For  this  purpose  take  a  glass  flask, 
or,  better,  a  bolt  head  (Fig.  65),  and  put  into 
it  water  enough  to  fill  the  stem  and  a  small  part 
of  the  bulb.  Invert  it  so  that  the  water  may  be 
boiled  by  holding  the  bulb  over  the  flame  of  a 
lamp.  Boil  it  until  the  steam  issues  freely  from 
the  stem,  and  then,  removing  it  from  the  flame, 
cork  the  stem  at  the  same  instant.  The  air  has 
been  driven  out  from  the  instrument,  and  noth- 
ing remains,  to  press  upon  the  water,  but  steam. 
Turn  the  bulb  upward  so  that  the  water  may  fill 
the  stem  ;  pour  cold  water  upon  the  bulb,  and  the 
water  inside  will  boil  violently.  Even  when  the 
tube  has  become  so  cold  that  it  may  be  handled 
without  inconvenience,  a  fresh  bath  of  cold  water 
will  cause  the  boiling  to  continue.  It  boils  at  the  low  tem- 
perature because  the  cold  water,  condensing  the  steam,  re- 
moves the  pressure  from  its  surface. 


>144 


NATUEAL   PHILOSOPHY. 


The  Temperature  stops  rising.  —  No  matter  how  much 
heat  may  be  applied  to  boiling  water,  its  temperature  is  not 
raised.  Moreover,  the  temperature  of  the  steam  is  always 
that  of  the  water  from  which  it  is  made. 

By  the  following  experiment  these  facts  maybe  illustrated. 
Water  is  placed  in  an  open  vessel  V  (Fig.  66).  Into  the 
water  is  plunged  the  bulb  of  an  air-thermometer  T,  whose 
tube  is  bent  twice  at  right  angles  for 
the  purpose.  While  the  water  is  being 
heated  by  a  lamp-flame,  the  gradual 
sinking  of  the  fluid  in  the  stem  of  the 
thermometer  shows  the  rise  of  tem- 
perature ;  but,  when  the  water  fairly 
boils,  the  fluid  stops  sinking,  showing 
that  the  temperature  no  longer  rises. 
The  fluid  will  remain  motionless  until 
the  water  in  the  vessel  has  been  changed 
to  steam.  Let  the  bulb  be  lifted  into 
the  steam  above  the  water  ;  no  change 
occurs  in  the  height  of  the  fluid  in  the 
stem,  hence  the  temperature  of  the 
steam  must  be  the  same  as  that  of 
the  water. 

But  the  Expansion  increases.  —  If  all  the  heat  applied 
to  a  boiling  liquid  is  expended  to  produce  expansion,  we 
may  expect  that  this  effect  will  be  more  rapid  than  when 
a  part  of  it  was  used  to  raise  the  temperature.  This  in- 
ference is  abundantly  verified.  Steam  fills  about  1,700 
times  as  much  space  as  the  water  from  which  it  was 
formed. 

The  Latent  Heat  of  Steam.  —  The  amount  of  heat  re- 
quired to  expand  water  into  steam,  in  other  words,  the  latent 
heat  of  steam,  is  very  great.  Bj7  accurate  experiment  it  has 
been  found  to  be  972°  F.  The  steam  and  the  boiling  water 
are  ot  the  same  temperature,  }Tet  there  is  an  excess  of  heat 
in  an  ounce  of  steam,  which,  if  applied  to  one  ounce  of  water, 


Fig.  66. 


NATURAL   PHILOSOPHY.  145. 

would  be  sufficient,  were  it  possible,  to  raise  its  temperature 
to  972°  ;  it  will  raise  the  temperature  of  nine  ounces  of  water 
108.° 

60.  The  heat  which  has  been  required  to  produce  expan- 
sion will  be  reproduced  when  the  expanded  body  again 
contracts. 

Heat  restored  after  being  used. — The  following  ex- 
periment very  satisfactorily  shows  that  heat  is  required  to 
produce  expansion,  and  that  it  is  again  given  off  when  con- 
traction occurs.  The  bulb  of  an  air-thermometer  is  placed 
in  a  receiver  over  the  plate  of  an  air-pump ;  the  stem,  pass- 
ing through  the  top  of  the  receiver,  is  bent  twice  at  right 
angles,  and  is  filled  with  its  colored  fluid  to  a  height  very 
carefully  marked.  By  a  few  rapid  strokes  of  the  piston,  the 
air  is  partly  exhausted  from  the  receiver  ;  that  which  remains 
expands,  and  the  rising  of  the  fluid  in  the  thermometer 
shows  that  the  bulb  is  at  the  same  time  cooled.  If,  now, 
air  be  allowed  to  return  to  the  receiver,  the  air  inside  be- 
comes more  dense,  and  the  sinking  of  the  fluid  in  the  ther- 
mometer shows  that  heat  is  again  given  off. 

Illustrations.  —  Numerous  familiar  facts  illustrate  this 
principle.  If  water  evaporates  from  the  hand,  it  cools  the 
hand,  because  the  hand  furnishes  the  heat  to  expand  the 
water  into  steam  ;  and,  when  vapor  condenses  upon  the  hand, 
the  hand  is  warmed,  because  the  vapor  gives  to  it  all  the 
heat  which  had  been  used  to  keep  the  water  in  the  form  of 
steam. 

Bodies  in  contact  with  melting  snow  or  ice  are  cooled, 
because  they  must  furnish  heat  to  change  the  solid  to  the 
liquid  form.  But  bodies  near  to  freezing  water  are  warmed, 
because  the  water,  while  freezing,  gives  up  the  heat  which 
had  been  needed  to  keep  it  in  a  fluid  form. 

Steam-Heating-.  —  In  the  production  of  steam  the  kinetic 
energy  of  the  fuel,  burning  in  the  furnace,  becomes  potential 
energy  in  the  expanded  steam.  Let  this  steam  be  condensed 


146  NATURAL   PHILOSOPHY. 

in  pipes,  and  its  potential  energ}^  is  changed  back  again  to 
kinetic  energy,  and  the  pipes  show  it  by  being  hot.  This 
principle  is  largely  applied  in  the  warming  of  buildings  by 
steam. 

REVIEW. 

I.  — SUMMARY   OF  PRINCIPLES. 

Conductivity  is  that  quality  of  a  substance  which  allows 
heat  to  pass  from  molecule  to  molecule  through  the  bod}T. 

Convection  is  the  transmission  of  heat  by  moving  parti- 
cles or  currents  in  the  substance. 

Solids  are  the  best  conductors,  liquids  stand  next  in  order, 
and  gases  last. 

Gases  are  heated  by  convection  only,  liquids  by  convection 
chiefly,  and  solids  by  convection  never. 

With  few  exceptions  the  volume  of  a  body  increases  with 
the  temperature. 

Solids  expand  least,  liquids  more,  and  gases  most,  by  the 
same  increment  of  heat. 

Thermometers  are  instruments  for  measuring  temperature. 
180°F.  =  100°  C.  =  80°  R. 

Fahrenheit°=f  Cent0.  +  32,  =  f  Reaumur0 -f32. 

Sensible  heat  is  the  kinetic  energy  of  the  molecular  motion. 
Latent  heat  is  the  potential  energy  due  to  the  separation  of 
molecules  by  heat. 

Sensible  heat  becomes  latent  during  the  melting  of  a  solid 
and  the  boiling  of  a  liquid. 

Latent  heat  becomes  sensible  during  the  liquefaction  of 
vapors  and  the  solidifj'ing  of  liquids. 

Equal  weights  of  any  two  substances  at  the  same  tempera- 
ture contain  different  quantities  of  heat. 

The  total  heat  in  a  body  compared  with  that  in  the  same 
weight  of  water  at  the  same  temperature  is  its  specific  heat. 

The  boiling  point  of  a  liquid  depends  on  its  purity,  on  the 
nature  of  the  vessel  containing  it,  and  on  the  pressure  upon  it. 


NATURAL   PHILOSOPHY,  147 

II. —SUMMARY    OF    TOPICS. 

53.  Conduction  of  heat. — Explanation. — Definitions. — 
Conductivity  of  metals.  — Of  liquids.  — Of  gases. 

54.  Convection    illustrated.  —  Defined.  —  Of    air.  —  Of 
liquids.  —  Of  solids. 

55.  The  twofold  action  of  heat.  —  Expansion  of  solids.  — 
Of  liquids.  —  Of  gases. 

56.  Temperature    measured    by   expansion.  —  The    ther- 
mometer. —  Fahrenheit's.  —  Centigrade.  —  Reaumur's.  — 
Degrees  below  zero.  —  Other  forms. 

57.  Effect  of  heat  on  the  motion  and  position  of  mole- 
cules. —  Sensible  and  latent  heat.  —  Specific  heat. 

58.  The   melting  point. — No   rise   of  temperature  while 
melting.  —  But   an   increased   expansion. — Except   in   the 
case  of  ice.  — The  latent  heat  of  water. 

59.  The   boiling  point.  —  Depends   on   the  purity  of  the 
liquid.  —  On  the  nature  of  the  vessel.  — And  on  the  press- 
ure.—  No  rise  of  temperature  during   ebullition. — But  an 
increased  expansion.  — The  latent  heat  of  steam. 

60.  Heat  restored    after  being    used.  —  Illustrations.  — 
Steam-heating. 


148  NATURAL  PHILOSOPHY. 


CHAPTER  VI. 
ON  UNDULATORY  ENERGY:   SOUND. 


SECTION   I. 
ON  THE  TRANSMISSION  AND  REFLECTION  OF  SOUND. 

61.  SOUND -WAVES  travel  through  all  elastic  media.  The 
Velocity  of  sound  is  not  the  same  in  different  substances  ;  it 
is  governed  b}T  two  Laws  :  — 

1st,  The  velocity  of  sound  varies  inversely  as  the  square 
root  of  the  density  of  the  substance. 

2d,  The  velocity  of  sound  varies  directly  as  the  square 
root  of  the  elasticity  of  the  substance. 

In  the  same  medium,  the  velocity  of  sound  is  uniform.  (G. 
226,  227;  A.  489-491.) 

Sound -Waves.  —  All  sounds  are  undulations,  but  it  is 
not  true  that  all  undulations  are  sound.  Some  are  too  slow 
to  affect  the  ear :  such  are  those  produced  by  the  vibrations 
of  a  cord  not  over- stretched.  On  the  other  hand,  there  are 
undulations  which  are  too  rapid  to  be  heard.  The  lower 
limit  has  been  fixed  at  sixteen  a  second,  and  the  higher  at 
38,000.  The  energy  of  waves  which  occur  within  these  limits 
of  velocity  can  affect  the  ear,  and  such  waves  are  called 
SOUND-WAVES,  or  simply,  SOUND. 

It  is  interesting  to  notice  that  the  limits  of  hearing  are  not 
the  same  in  all  persons.  "  Nothing  can  be  more  surprising 
than  to  see  two  persons,  neither  of  them  deaf,  the  one -com- 
plaining of  the  penetrating  shrillness  of  a  sound,  while  the 
other  maintains  that  there  is  no  sound  at  all."  "In  the 


NATUBAL  PHILOSOPHY. 


149 


*  Glaciers  of  the  Alps '  I  have  referred  to  a  case  of  short 
auditory  range  noticed  by  myself  in  crossing  the  Wengern 
Alp  in  company  with  a  friend.  The  grass  at  each  side  of 
the  path  swarmed  with  insects  which,  to  me,  rent  the  air 
with  their  shrill  chirruping.  My  friend  heard  nothing  of 
this,  the  insect-music  tying  quite  bej'ond  his  range  of  audi- 
tion." (See  Tyndall's  Lectures  on  Sound.) 

Are  transmitted  through  all  elastic  Bodies.  —  Nu- 
merous facts,  easily  verified,  prove  that  sound-waves  can 
traverse  all  elastic  bodies.  When,  for  example,  the  blows  of 
a  hammer  fall  upon  one  end  of  a  long  wooden  beam,  an  ear 
placed  in  contact  with  the  other  end  hears  the  sound  with  sur- 
prising distinctness.  The  same  thing  is  true  of  other  solid 
bodies.  The  clatter  of  horses'  hoofs,  or  the  rattle  of  a  rail- 
way-train, quite  inaudible  to  one  who  stands  erect,  is  heard 
distinctly  when  the  ear  is  placed  in  contact  with  the  ground. 
The  solid  earth,  in  this  case,  transmits  the  sound-waves. 

In  liquids,  also,  sound-waves  travel  freely.  Let  two  stones 
be  struck  together  under  water ;  the  sound  will  be  heard  by 
an  ear,  itself  under  water,  a  long  distance  away. 

The  transmission  of  sound-waves  through  gases  is  suffi- 
ciently familiar ;  the  sounds  which  throng  the  ear  so  con- 
stantty  are  transmitted  through  the  atmosphere. 

The  Velocity  not  the  same  in  all  Media.  —  The  velo- 
city of  sound  in  a  great  many  substances  has  been  found 
by  laborious  and  skillful  experiments  (see  T}*ndairs  Lectures 
on  Sound).  In  the  following  table  some  of  these  results 
are  collected  :  — 


SUBSTANCES. 

TEMPERATURE. 

VELOCITY. 

Air    

32°  F. 
61°     « 

32°    « 
32°     ' 
59°    ' 

68°     « 

1,092  fe 
1,118 
1,040 
4,164 
4,714 
16,822 
10,900 

cjt  p< 

>rsec. 

Air                                     .                       ... 

River-water    

Pine  Wood     

150  NATURAL  PHILOSOPHY. 

The  velocity  of  sound  depends  upon  the  density  and  the 
elasticity  of  the  medium  in  which  it  travels. 

The  first  Law.  —  The  density  of  oxygen,  other  things 
being  equal,  is  about  sixteen  times  that  of  h}'drogen.  But 
we  see  in  the  table  that  the  velocity  of  sound  in  oxygen  is 
only  about  one-fourth  as  great  as  in  hydrogen.  In  this  case 
the  velocity  is  inversely  as  the  square  root  of  the  density  of 
the  medium.  It  is  always  so.  The  law  has  been  verified  by 
repeated  experiments. 

The  second  Law.  —  When  air  is  heated  in  a  tight  vessel, 
its  elasticity  is  increased,  while  its  density  is  unchanged. 
In  this  condition  it  will  conduct  sound  more  rapidly.  If  the 
elasticity  of  air  be  made  four  times  as  great,  the  velocity  of 
sound  will  be  doubled.  The  velocity  of  sound  in  this  case  is 
directly  as  the  square  root  of  the  elasticity  of  the  medium. 
It  is  so  in  all  cases. 

Density  and  Elasticity.  —  It  is  evident  that  both  density 
and  elasticity  must  be  known,  before  we  can  judge  the  power 
of  a  substance  to  conduct  sound.  Liquids  are,  for  example, 
more  dense  than  gases :  their  conducting  power,  on  this 
account,  would  be  less  ;  but,  on  the  other  hand,  their  elas- 
ticit}^  measured  by  the  force  required  to  compress  them  is 
vastly  greater,  so  that,  as  the  table  shows,  water  conducts 
sound  better  than  air. 

But  in  the  same  Medium  Velocity  is  Uniform.  — 
The  velocity  of  sound-waves  in  air  or  in  water,  for  example, 
is  uniform.  Moreover,  all  sounds  in  the  same  medium 
travel  with  the  same  velocit}7.1  When  we  listen  to  the 
music  of  a  distant  band,  the  various  notes,  high  and  low, 
loud  and  soft,  reach  the  ear  in  the  same  order  in  which  they 
were  made.  So  also  the  shrill  chirping  of  insects,  the  dull 
thud  of  a  falling  stone,  the  melodious  songs  of  the  birds, 
and  the  murmur  of  rivulets,  are  all  borne  with  equal  swift- 
ness through  the  air. 

1  There  is  reason  to  believe  that  very  loud  sounds  do  travel  a  very  little  faster  than 
feeble  ones. 


NATURAL  PHILOSOPHY. 


151 


Application.  —  So  uniform  is  the  velocit}7  of  sound,  that 
distances  may  be  measured  by  means  of  it.  Suppose  the 
flash  of  a  cannon  on  a  distant  hill  was  seen,  and  in  ten  sec- 
onds afterward  the  report  was  heard,  the  temperature  at  the 
time  being  61°  F.  The  velocity  of  sound  is  1,118  feet ;  and 
the  sound-waves,  starting  when  the  flash  was  seen,  took  ten 
seconds  to  reach  the  ear.  1,118x10  =  11,180.  The  ob- 
server was  at  a  distance  of  11,180  feet  from  the  cannon. 

The  Formula.  —  The  two  laws  of  velocity  are  expressed 
in  the  formula  :  — 

V=     fl 

Nd 

The  Effect  of  Temperature.  —  The  heating  of  air  ex- 
pands it :  its  elasticity  is  thereby  increased,  and  its  density 

diminished.    But  to  increase  the  value  of  e,  and  lessen  that  of 

(> 
d,  would,  in  both  cases,  increase  the  value  of  the  fraction  - . 

Hence  a  rise  of  temperature  must  increase  the  velocity  of 
sound. 

This  is  verified  by  experiment.  Notice  the  two  velocities 
of  air  in  the  table.  * 


M 


62.  When  sound-waves  fall  upon  the  surface  of  a  second 
medium,  only  a  part  of  them  enter :  the  rest  are  reflected. 
The  Reflection  of  sound  is  governed  by  the  following  Law  :  — 

The  angle  of  reflection  must  be  equal  to 
the  angle  of  incidence. 

An  Echo  is  produced  by  the  reflection  of 
sound.  (G.  231,  232  ;  A.  495,  496.) 

The  Reflection  of  Sound.  —  To  illus- 
trate the  reflection  of  sound,  suppose  the  line 
I  A  (Fig.  67)  to  represent  the  direction  of 
several  sound-waves,  which,  passing  through 
the  air,  strike  a  body  M  M.  Some  of  these 
waves  will  pass  through  the  body,  but  others  will  be 


Fig.  67. 


152  NATURAL  PHILOSOPHY. 

thrown  off  in  the  direction  A  R.  These  are  the  reflected 
waves. 

Now,  a  person  standing  at  R  will  hear  the  voice  of  another 
at  I,  when  the  distance  is  considerable,  sounding  as  though 
it  came  from  a  person  in  the  direction  R  A.  We  always 
judge  the  direction  of  a  sounding  body  from  us,  to  be  that 
from  which  the  waves  enter  the  ear. 

The  Law  of  Reflection.  —  To  understand  the  language 
of  this  law,  let  us  refer  again  to  Fig.  67.  The  waves 
I  A,  those  which  fall  upon  the  reflecting  surface,  are  called 
the  INCIDENT  waves :  the  waves  A  R,  those  that  are  thrown 
off  from  the  surface,  are  called  the  REFLECTED  waves ;  and 
the  point  A  is  called  the  POINT  OF  INCIDENCE.  Now,  if  a 
perpendicular,  A  P,  be  drawn  to  the  reflecting  surface  at  the 
point  of  incidence,  then  the  angle  I  A  P  is  the  ANGLE  OF  IN- 
CIDENCE, and  the  angle  P  A  R  is  the  ANGLE  OF  REFLECTION. 
The  law  of  reflection  requires  that  these  angles  shall  always 
be  equal. 

The  Echo.  —  An  echo  is  a  repetition  of  sound  produced 
by  the  reflection  of  waves  from  a  distant  object.  Who, 
after  loudly  uttering  a  word  or  sentence,  has  not  sometimes 
listened  to  the  sound  of  his  own  voice  coming  back  to  him 
from  a  distant  wood,  or  from  the  face  of  a  cliff,  or,  it  may 
be,  from  the  wall  of  a  distant  building?  Visitors  to  Coopers- 
town,  N.Y.,  will  not  soon  forget  the  fine  echo  returned  from 
the  rocky  hills  which  skirt  Otsego  Lake.  There,  we  are  told 
by  Fenimore  Cooper,  once  dwelt  Natty  Bumpo,  the  hero  in 
the  story  of  "  The  Pioneers."  Let  his  name  be  loudly  called 
from  a  certain  place  upon  the  lake,  and  immediately  the  re- 
sponse, "Nat-ty-Bum-po,"  every  syllable  full  and  clear,  rings 
back  over  the  water  as  if  spoken  by  the  hero  himself  from 
his  cave  in  the  cliffs. 

Multiple  Echo.  —  When  two  obstacles  are  opposite  to 
one  another,  the  sound  ma}r  be  reflected  back  and  forth  many 
times.  Surprising  repetitions  of  echoes  are  in  this  way 
sometimes  produced.  It  is  said  that  an  echo  near  Milan 


NATURAL  PHILOSOPHY.  153 

repeats  a  single  sound  thirty  times.  "When  a  trumpet  is 
sounded  at  the  proper  place  in  the  Gap  of  Dunloe,  the 
sonorous  waves  reach  the  ear  after  one,  two,  three,  or  more 
reflections  from  the  adjacent  cliffs,  and  thus  die  away  in  the 
sweetest  cadences." 

SECTION  II. 

ON  MUSICAL  SOUNDS. 

63.  Musical  sounds  are  caused  by  rapid  vibrations  which 
follow  each  other  with  great  regularity.  Any  noise  what- 
ever, when  repeated  rapidly,  will  cause  a  continuous  tone : 
even  separate  puffs  of  air,  following  each  other  rapidl}',  pro- 
duce a  musical  sound.  (G.  236,  237  ;  A.  512.) 

Musical  Sounds.  —  When  a  single  and  intense  air-wave 
is  suddenly  produced,  as  when  a  gun  is  fired,  the  resulting 
sound  is  called  a  REPORT.  Let  a  series  of  such  sounds  be 
made  in  quick  but  irregular  succession,  and  the  resulting 
sound  is  called  NOISE.  But  when  the  waves  are  made  with 
regularity,  and  follow  each  other  so  swiftly  that  the  ear  can 
distinguish  no  interval  of  time  between  them,  the  result  is  a 
MUSICAL  SOUND. 

Any  Noise  repeated  rapidly  causes  a  continuous 
Tone.  —  No  matter  what  the  source  of  the  waves  maybe, 
nor  how  unmusical  the  separate  noises :  only  let  them  be 
repeated  with  regularity  and  rapidity,  and  they  will  result 
in  music.  Slowly  pass  a  piece  of  ivory,  or  even  the  finger- 
nail, over  the  rough  surface  of  a  wound  piano-wire,  and  the 
sound  of  its  strokes  against  the  separate  ridges  is  altogether 
unpleasant ;  but  pass  it  quickly  over  the  same  surface,  and 
the  ear  is  saluted  with  a  musical  tone  of  surprising  shrillness 
and  purity.  If  a  card  be  pressed  against  the  teeth  of  a 
wheel  which  rotates  slowly,  a  series  of  distinct  and  unpleas- 
ant taps  will  be  heard ;  but  if,  by  means  of  a  larger  wheel 
and  band,  this  wheel  be  made  to  revolve  rapidly,  the  taps 
will  coalesce,  and  salute  the  ear  with  music. 


154 


NATURAL  PHILOSOPHY. 


Even  Puffs  of  Air :  the  Siren.  —  The  siren  is  an  in- 
strument by  which  ;i  scries  of  air-putt's  arc,  made  to  produce 
a  musical  sound,  and  by  which  the  number  of  puffs  made  in 
a  second  are  registered.  Its  structure  may  be  learned  from 
Fig.  68. 

Description.  —  A  brass  tube,  O,  leads  from  a  wind-chest, 
E,  to  a  brass  plate,  B,  which  is  pierced  with  a  series  of 

holes  arranged  around  the  cir- 
cumference of  a  circle.  Above 
this  plate  is  a  disk,  also  per- 
forated with  holes  exactly  cor- 
responding to  those  in  the  plate 
below.  The  disk  is  provided 
with  a  vertical  steel  axis,  and 
is  so  fixed  that  it  may  rotate 
with  a  very  small  amount  of 
friction.  The  wheel-work  shown 
in  the  upper  part  of  the  figure 
registers  the  number  of  puffs 
made  in  any  given  time. 

Its  Action.  — Now,  when  the 
disk  revolves,  the  holes  in  it 
will  be  brought  alternately  over 
the  perforations  in  the  plate  B,  and  the  spaces  between  them, 
so  that  these  holes  will  be  alternately  opened  and  closed. 
When  the  disk  is  still,  and  the  holes  are  open,  if  air  be  urged 
through  the  tube  O,  it  will  escape  from  the  top  in  steady 
streams,  but  when  the  disk  revolves  these  streams  will  be  cut 
up  into  successive  puffs.  If  the  disk  turns  slowly,  the  sepa- 
rate puffs  are  heard ;  but,  as  the  disk  is  turned  more  and 
more  rapidly,  the  air  announces  its  escape  by  a  musical  sound 
of  great  purity  and  increasing  shrillness. 

By  a  simple  artifice,  the  air  which  gives  the  sound  is  made 
to  turn  the  disk.  This  is  done  by  making  the  holes  through 
the  plate  B  oblique  instead  of  vertical ;  those  in  the  disk 
being  also  oblique,  but  inclined  in  the  opposite  direction. 


Pig.  68. 


NATURAL    PHILOSOPHY.  155 

64.  Musical  sounds  differ  in  throe  respects:  in  1'itch  ; 
in  Intensity;  and,  in  Quality. 

I. —PITCH. 

Pitch  depends  entirely  upon  the  rapidity  of  vibrations 
which  produce  the  sound. 

The  difference  in  the  pitch  of  two  sounds  is  called  an  IN- 
II.UVAL;  and  a  series  of  eight  sounds  of  different  pitch  has 
been  adopted  as  the  foundation  of  all  music,  and  called  the 
DIATONIC  SCALE. 

The  Number  of  vibrations  to  produce  the  note  A  of  the 
treble  clef  is  440  a  second.  (G.  243-248  ;  A.  520.) 

Pitch  depends  on  the  Rapidity  of  Vibration.  —  The 

pitch  of  sounds  is  that  which  distinguishes  them  as  being 
high  or  low.  It  depends  entirely  upon  the  rapidity  of  vibra- 
tion :  the  more  rapid  the  vibrations,  the  higher  will  be  the 
sound  produced.  Two  sounds  made  by  the  same  number  of 
vibrations  per  second,  however  much  they  may  differ  in  other 
respects,  will  have  the  same  pitch. 

Intervals.  —  When  the  number  of  vibrations  which  pro- 
duce one  sound  is  twice  as  great  as  that  which  produces 
another,  we  must  not  say  that  the  sound  is  twice  as  //,/>/ A, 
but  rather  that  it  is  an  octave  above.  The  term  "  octave  "is 
used  to  designate  a  tone  which  is  made  by  twice  the  number 
of  vibrations  needed  to  produce  a  lower  one,  called  the  fun- 
damental. Other  intervals  will  be  named  in  the  description 
of  the  scale. 

The  Diatonic  Scale.  —  Now,  the  difference  in  pitch,  or 
the  interval  between  a  fundamental  note  and  its  octave, 
is  very  great.  To  fill  up  this  interval,  sounds  have  been 
chosen  which  blend,  or  harmonize  most  perfectly,  with  the 
fundamental,  or  with  each  other.  These,  placed  between  the 
fundamental  and  its  octave,  form  a  series  of  eight  tones, 
called  the  NATURAL  or  the  DIATONIC  SCALE. 

The  eight  notes  of  the  scale  are  expressed  by  the  follow- 
ing names  and  intervals :  — 


156 


NATURAL   PHILOSOPHY. 


Names,         C,    D,    E,    F,    G,    A,    B,    C. 
Intervals,  1st,  2d,  3d,  4th,  5th,  6th,  7th,  8th. 
This  scale  repeated  about  eleven  times,  making  what  is 
termed  in  music  eleven  octaves,  will  include  all  sounds  with- 
in the  range  of  the  human  ear.     Only  about  seven  octaves 
are  used  in  music. 

The  method  of  representing  the  notes  in  music  is  familiar 
to  all.  Remember  that  the  note  called  A  is  found  in  the 
second  space  of  the  treble  clef,  and  the  position  of  all  others 
may  be  easily  traced. 

Number   of   Vibrations   for  the  Notes.  —  The    num- 

ber of  vibrations  to 
produce  the  various 
notes  may  be  found 
by  experiment  with 
the  siren.  (See 
Tyndall  on  Sound.) 
Or  it  may  be  found 
with  the  greatest  ac- 
curacy by  means  of 
the  electric  register 
(Fig.  52).  Fig.  69 
shows  how  the  standard  tuning-fork  is  made  to  open  and 
close  the  electric  circuit.1 

1  From  the  prong  of  the  fork  a  silk  fiber  stretches  across  to  a  slender  vertical 
spring,  s,  fixed  at  the  lower  end,  while  its  upper  end  rests  against  the  end  of  a  set 
screw,  t.  The  two  surfaces  in  contact  are  platinized.  The  spring  is  slightly  bent; 
and  the  set  screw,  pressing  against  its  upper  end,  holds  it  in  constant  tension,  and 
thus  forbids  it  vibrating,  except  in  unison  with  the  fork.  Every  vibration  of  the 
prong  is  transmitted  by  the  fiber,  and  compels  the  spring  away  from  contact  with 
the  screw.  Putting  this  break-circuit  in  place  of  the  monocord,  represented  in  Fig. 
52,  between  the  pendulum  P  and  the  register  R,  the  vibrations  of  the  fork  record 
themselves  upon  the  moving  paper. 

Noticing  that  the  accuracy  of  Koenig's  tuning-forks  is  questioned  by  Mr.  Ellis 
(Nature,  xvi.,  p.  85),  I  fancied  that  the  testimony  of  this  method  would  not  be  with- 
out interest.  Seizing  the  earliest  opportunity,  therefore,  I  submitted  the  C^sfork, 
bearing  Koenig's  monogram,  to  careful  examination.  The  pendulum  was  accurately 
adjusted  to  hold  the  circuit  one-half  a  second.  The  iodide-starch  solution,  with  a 
battery  of  ten  Bunsen's  immersion  cells,  was  used.  Fifteen  perfectly  distinct  and 
easily  counted  records  were  taken.  Every  one  of  these  autographs  was  found  to 
consist  of  128  dots,  representing  128  complete  vibrations  per  half-second,  or  256  per 
second,  testifying  to  the  exactness  of  Koenig's  stamu.  Jour-  Jfrank.  Ind.  vol.  Ixxii. 


NATURAL   PHILOSOPHY.  157 

On  the  English  standard  of  pitch,  the  note  A  of  the  treble 
clef  is  made  by  440  vibrations  a  second. 

On  the  French  standard  the  rate  for  the  same  note  is  435. 

Relative  Kates.  —  If  we  represent  the  number  of  vibra- 
tions for  the  fundamental  note  by  1,  then  the  several  notes 
of  the  scale  will  be  made  by  the  following  ratios :  — 
C,  D,  E,  F,  G,  A,  B,  C. 

i»  *»  f>  t»  f>  *»  ¥->  2- 

Absolute  Rates.  —  Now,  remembering  this  series  of 
fractions,  and  the  fact  that  A  is  made  by  440,  the  number 
of  vibrations  for  all  the  others  may  be  found.  Thus,  for 
example,  how  many  vibrations  to  give  the  fundamental  C? 
The  relative  number  of  vibrations  for  A  and  C  are  -|  and  1  ; 
that  is,  A  is  produced  *by  f  as  many  vibrations  as  C  ;  or,  to 
reverse  the  ratio,  C  requires  |-  as  many  as  A,  and  -|x440  = 
264.  Having  this  number  for  the  fundamental,  multiply  this 
by  the  fractions  £,  j,  f ,  &c. ,  and  the  numbers  for  the  cor- 
responding notes  will  be  obtained.  These  multiplied  by  2 
will  give  the  numbers  for  the  notes  in  the  next  higher  octave  ; 
or,  divided  by  2,  will  give  the  numbers  for  the  notes  in  the 
octave  below. 

II.  —  INTENSITY. 

Definition.  —  The  intensity  of  sound  is  that  which  dis- 
tinguishes it  as  being  loud  or  soft.  It  is  the  energy  of  the 
waves  against  the  ear.  It  depends  entirely  upon  the  ampli- 
tude of  the  vibrations  which  produce  it.  The  greater  the 
amplitude,  the  louder  the  sound  will  be.  In  the  case  of  a 
vibrating  string,  for  example,  the  loudness  or  intensity  of 
the  sound  made  by  it  will  depend  entirely  upon  the  distance 
through  which  the  string  vibrates  across  its  line  of  rest. 
(G.  222,  223.) 

The  Law.  —  If  this  distance  be  doubled,  then  the  velocity 
of  a  string  will  be  doubled  also.  But  a  body  with  double 
velocity  has  a  quadruple  energy.  Hence  the  intensity  of 
sound  varies  as  the  square  of  the  amplitude. 


158 


NATURAL   PHILOSOPHY. 


III.  —  QUALITY. 

Definition.  —  By  quality,  we  refer  to  that  peculiarity  of 
sound  by  which  we  may  distinguish  notes  of  the  same  pitch 
and  intensity,  made  on  different  instruments.  The  pitch  and 
intensity  of  notes  made  on  a  violin  and  on  a  piano  may  not 
differ,  and  yet  how  easy  to  tell  the  sounds  apart !  We  rec- 
ognize the  voices  of  friends,  not  by  their  pitch  nor  their 
intensity,  but  by  their  quality.  (G.  249,  253-255  ;  A.  523- 
526.) 

Compound  Sounds.  —  A  musical  sound  is  rarely  made 
by  a  single  undulation :  several,  with  different  rates  and 
amplitudes,  are  combined  in  almost  every  tone  we  hear. 


Fig.  70» 

Illustration.  —  If  a  plate  of  brass  is  fastened  at  its  cen- 
ter, and  covered  with  a  sprinkling  of  fine  sand,  and  then  if 
a  violin-bow  is  drawn  across  its  edge  (Fig.  70),  a  shrill 
tone  is  produced.  The  sand  at  the  same  time  dances  about 


NATURAL   PHILOSOPHY. 


159 


in  a  curious  manner,  and  finally  arranges  itself  in  straight 
lines  and  curves  upon  the  plate. 

The  sand  gathers  where  there  is  least  vibration,  and  shows 
that  the  plate  vibrates  in  segments  (p.  104) .  The  plate  in 
the  cut  shows  eight  segments. 

Now,  each  of  these  vibrating  parts  starts  an  undulation  in 
the  air,  and  consequently  there  are  eight  different  sounds 
combined  in  the  one  shrill  tone  which  is  heard. 

Overtones.  —  Whenever  a  piano- wire  or  the  cord  of  a 
harp  is  struck,  it  vibrates  as  a  whole  and  in  segments  at  the 
same  time. 

Its  vibration  as  a  whole  j'ields  its  fundamental  tone. 

Its  vibrations  in  segments  yield  higher  tones,  called  OVER- 
TONES, or  sometimes  HARMONICS. 

The  fundamental  with  its  overtones  are  combined  in  the 
sound  which  is  heard  whenever  the  wire  or  cord  is  struck. 

Helmholtz'  Theory.  —  The  quality  of  a  sound  depends 
on  the  number  and  prominence  of  the  different  undulations 
which  are  combined  to  produce  it. 

Each  different  set  of  undulations  produces  a  resultant  wave 
of  a  different/orm,  and       x'/\ 
these  waves  of  differ-    /  /     \ 
ent  form  affect  the  ear    *\ 
as  sounds  of  different 
quality. 

65.  The  Phonograph 
is  an  instrument  for 
recording  and  reprodu- 
cing sounds.  It  acts  on 
the  principle  that  waves 
of  the  same  rate,  am- 
plitude, and  form  are 
exactly  the  same  sound.  Pig.  71. 

The  Phonograph.  —  The  construction  of  Edison's  phono- 
graph or  "  talking-machine  "  is  shown  in  Figs.  71  and  72. 


160 


NATURAL   PHILOSOPHY. 


A  spiral  groove  is  cut  around  a  cylinder  of  metal,  A, 
which  may  be  turned  with  a  crank.  On  one  end  of  its  axle 
a  screw-thread  is  cut,  so  that  when  the  cylinder  is  turned  it 
is  at  the  same  time  moved  forward.  In  front  of  this  cylinder 
is  a  mouthpiece,  B,  with  a  thin  disk  of  metal,  C,  which  the 
voice  will  vibrate,  and  between  the  disk  and  the  cylinder  is  a 
needle-point  p  which  vibrates  with  the  disk. 

To  record  the  Voice.  —  A  sheet  of  tinfoil  is  wrapped 
smoothty  around  the  cj'linder,  and  the  mouthpiece  is  then 
adjusted  so  that  the  needle-point  will  press  lightly  against 
its  surface  just  over  the  spiral  groove.  The  speaker  then 
talks  loudly  into  the  mouthpiece  while  the  C3'linder  is  turned. 
The  air- waves  of  the  voice  vibrate  the  disk  ;  and  the  vibrat- 
ing disk  drives  the  needle-point  against  the  tinfoil,  and 
presses  it  to  greater  and  less  depths  into  the  groove.  This 
tracing  of  the  needle  is  a  record  of  the  voice. 

The  closeness  of  the  depressions  represents  the  pitch. 
The  depth  of  the  depressions  represents  the  loudness. 
The  form  of  the  depressions  represents  the  quality. 
To  reproduce  the  Voice.  —  Move  the  mouthpiece  so  that 
the  point   no   longer  touches  the  tinfoil,  and  turn  the  cyl- 
inder back  to 
the    place    it 
was   in  when 
the  record  be- 
gan.      Then 
again    bring 
the    point    in 
contact  with 

.  72.  the  tinfoil  and 

turn  the  cylinder  forward  exactly  as  at  first.  The  needle- 
point will  follow  the  tracing  which  it  made  before,  and  in 
going  over  the  prominences  and  into  the  depressions  will  com- 
pel the  disk  to  repeat  the  same  vibrations  which  it  made  be- 
fore under  the  influence  of  the  voice.  These  vibrations  of  the 
disk  reproduce  the  air-waves  which  the  voice  threw  against  it* 


NATURAL   PHILOSOPHY.  161 

and  if  the  ear  be  placed  near  the  mouthpiece,  or,  better  still, 
if  a  large  cone,  shown  by  dotted  lines  in  Fig.  71,  be  used,  the 
utterances  of  the  speaker  will  be  repeated  by  the  phonograph. 

66.  Musical  instruments  are,  for  the  most  part,  of  two 
classes :  first,  those  in  which  the  sounds  are  produced  by 
vibrating  strings,  and,  second,  those  in  which  sounds  are 
made  by  vibrating  columns  of  air. 

I.  —  STRINGED   INSTRUMENTS. 

Stringed  Instruments.  —  The  violin,  the  guitar,  and  the 
piano  are  familiar  forms  of  stringed  instruments.  In  every 
case,  cords  or  wires  are  tightly  stretched  over  some  solid  body 
having  considerable  surface.  The  music  of  these  instruments 
is  not  made  by  the  vibrations  of  their  cords  alone  :  the  sim- 
ple vibration  of  a  cord  is  not  able  to  produce  sound  of  suffi- 
cient intensit}^ ;  but  by  being  stretched  over  hollow  boxes  made 
of  elastic  wood,  the  material  of  the  box,  and  the  air  inside  of 
it,  are  made  to  vibrate,  and  these  vibrations,  joined  with  those 
of  the  cords,  produce  the  sounds  of  the  instrument. 

Pitch  varied  by  using  Strings  of  different  Lengths. 
—  The  pitch  of  any  sound  depends  upon  the  rapidity  of 
vibrations  ;  but  according  to  the  first  law  of  vibrating  strings, 
the  rapidity  of  vibration  is  greater  as  the  string  is  made 
shorter.  To  obtain  sounds  of  different  pitch,  we  may,  then, 
use  strings  of  different  lengths. 

Illustration.  —  Suppose  we  wish  to  know  the  lengths  of 
eight  strings  of  the  same  weight  and  tension,  which  will 
give  the  eight  notes  of  the  scale.  We  have  learned  that 
the  number  of  vibrations  per  second  is  inversely  as  the  length 
of  the  cord,  and  we  have  learned  also  that  the  relative  num- 
bers of  vibrations  for  the  eight  notes  are  expressed  by  the 
series  1,  f,  j,  f ,  f ,  f,  -^-,  2.  Then  invert  the  terms  of  this 
series,  and  they  must  express  the  relative  lengths  of  cord 
to  produce  the  notes.  They  will  be  1,  f,  f,  f,  f,  f,  ^,  J. 
Knowing  the  length  of  the  string  to  give  the  fundamental, 


162  NATUKAL   PHILOSOPHY. 

it  is  easy  to  calculate  the  lengths  of  all  the  others.  Let  us 
start  with  a  string  18  inches  long  for  the  first  note  ;  the 
second  must  be  f  x  18  ;  the  third  must  be  ^x  18  ;  the  fourth 
must  be  |x!8  ;  and  so  on  until  the  eighth,  which  must  be 
1x18. 

Pitch  is  varied  by  using  String's  of  different  Tension. 

—  According  to  the  second  law  of  vibrating  strings,  the  num- 
ber of  vibrations  made  in  a  second  increases  when  the  ten- 
sion increases.     Hence  the  pitch  of  sound  made  by  the  string 
will  be  higher  when  the  tension  is  made  greater. 

Pitch  is  varied  by  using  Strings  of  different  Weights. 

—  According  to  the  third  law  of  vibrating  strings,  the  num- 
ber of  vibrations  made  in  one  second  varies  inversely  as  the 
square  root  of  the  weight  of  the  strings.     Hence  the  pitch 
of  the  sound  will  be  higher,  when  the  string  which  makes  it 
is  lighter. 

II.  —  WIND-INSTRUMENTS. 

Wind-instruments.  —  The  organ  and  the  clarionet  are 
examples  of  wind-instruments.  In  the  organ,  sounds  are 
made  by  vibrating  columns  of  air  in  pipes,  sometimes  aided 
by  the  vibrations  of  a  slender  and  elastic  tongue,  called 
a  reed.  (See  T}^ndall  on  Sound.)  In  the  clarionet  the 
sounds  are  always  made  by  air-vibrations  aided  by  a  reed. 

Organ-Pipes.  —  The  pitch  of  sounds  in  pipes  depends 
upon  the  lengths  of  the  pipes.  A  pipe,  to  produce  the  lowest 
note  used  in  music,  must  be  thirty-two  feet  in  length,  and 
the  pitch  of  tones  from  other  pipes  will  vary  inversely  as  the 
lengths  of  the  pipes. 

Organ-pipes  are  sometimes  open  at  the  top,  and  sometimes 
closed.  An  open  organ-pipe  }Tields  a  note  an  octave  higher 
than  a  closed  pipe  of  the  same  length.  A  closed  pipe,  to 
give  the  lowest  note  in  music,  need  only  be  sixteen  feet  in 
length. 


NATURAL  PHILOSOPHY. 


163 


SECTION    III. 

ON   MUSICAL  AND   SENSITIVE   FLAMES. 

67.  When  a  gas-flame  burns  within  a  glass  tube,  a  musical 
sound  is  produced.  The 
pitch  of  the  tone  depends 
on  the  length  of  the  tube 
and  the  size  of  the  flame. 
A  silent  flame  may  be 
made  to  sing  by  sound- 
ing near  it  the  note  of 
the  tube.  Naked  flames 
are  also  sensitive  to  the 
action  of  neighboring 
sounds.  (G.  281.) 

The  Musical 
Flame.  —  Let  a  flame  of 
common  coal-gas,  placed 
under  the  end  of  a  glass 
tube  T  (Fig.  73),  be 
slowly  raised  into  it ; 
when  a  particular  height 
is  reached,  the  flame,  if 
small  enough,  will  burst 
forth  into  a  loud  and 
continuous  sound.  This 
sound  is  often  harsh, 
sometimes  melodious. 


Fig.  73. 


At  the  beginning  it  is  sometimes  low  and  smooth,  like  the 
whistle  of  a  very  distant  locomotive  ;  but,  as  the  experiment 
goes  on,  the  intensity  of  the  sound  rapidly  increases  until, 
like  the  long  monotonous  screech  of  the  engine  at  hand,  it 
becomes  almost  unbearable. 


164  NATURAL   PHILOSOPHY. 

In  tubes  of  tin  and  pasteboard,  sounds  of  different  quality 
are  obtained. 

"Explanation.  —  That  a  gas-flame  flutters  when  exposed 
to  a  gentle  breeze,  is  a  fact  sufficiently  familiar.  Now,  this 
fluttering  flame,  like  a  vibrating  tongue  or  reed,  must  cause 
Aribrations  in  the  air  around  it.  This  is  the  key  to  the  ex- 
planation of  musical  flames. 

The  air  in  the  tube  is  heated  by  the  flame  ;  it  rises,  and 
an  upward  current  through  the  tube  is  thus  produced.  The 
flame  flutters  in  this  current,  and  causes  a  system  of  waves, 
whose  rapidity  and  amplitude  give  pitch  and  intensity  to  the 
note  produced.  If  we  inquire  further  about  the  cause  of  the 
fluttering,  we  are  told  that  experiments  by  Faraday  proved 
that  gas  issues  from  a  burner  in  an  unsteady  stream,  due  to 
the  friction  against  the  sides  of  the  tube,  and  that  in  burn- 
ing it  makes  a  series  of  inaudible  explosions.  A  current 
of  air  heightens  both  of  these  effects,  and  makes  them 
sensible. 

Evidence  that  the  Flame  is  intermittent.  —  That  a 
musical  flame  is  thus  intermittent,  is  shown  by  the  following 
beautiful  experiment.  The  tube  T  (Fig.  74)  is  blackened  so 
as  to  keep  the  light  from  falling  on  the  screen  placed  behind 
it  at  S.  A  concave  mirror  M,  in  front  of  the  flame,  forms 
an  inverted  image  of  it  on  the  screen.  If  the  mirror  is 
turned  horizontally,  while  the  flame  is  silent  and  steady,  the 
image  will  move,  and  if  the  motion  of  the  mirror  is  swift,  an 
unbroken  band  of  light  will  be  seen  on  the  screen.  But  if, 
when  the  flame  is  singing,  the  mirror  is  swiftly  turned,  a 
series  of  distinct  images  will  appear. 

The  Pitch  of  the  Note.  —  In  these  tubes,  as  in  organ- 
pipes,  the  pitch  of  the  sound  depends  upon  the  length  of  the 
tube.  But,  while  the  pitch  depends  chiefly  upon  the  length 
of  the  tube,  it  is  partly  governed  b}7  the  size  of  the  flame. 
If  one  tube  is  just  twice  the  length  of  another,  its  funda- 
mental note  is  an  octave  below  ;  but,  when  placed  over  a 
flame  whose  size  fits  it  to  sing  in  the  shorter  tube,  the  note 


NATURAL  PHILOSOPHY. 


165 


of  the  shorter  tube  will  be  produced.  Then  let  the  flame 
be  gradually  emarged,  and  in  a  little  time  the  low  funda- 
mental note  of  the  tube  suddenly  bursts  forth.  By  varying 


Fig.  74. 

the  size  of  the  flame  it  is  possible  to  obtain  the  fundamental 

note,  its  octave,  and  its  four  harmonics,  from  the  same  tube. 

Sensitive  Flames.  —  The   name    ' '  sensitive  flames  ' '    is 

given  to  those  which,  without  being  inclosed  in  tubes,  are 


166 


NATURAL  PHILOSOPHY. 


affected  by  sounds.  Certain  sounds  in  an  instrumental  con- 
cert often  cause  curious  motions  of  the  gas-flames  in  the 
room.  This  observation  was  first  published  in  1858.  The 
motions  referred  to  consist  of  a  u  jumping  "  of  the  flame  to 
considerable  height,  or  a  thrusting  forth  of  tongues  of  flame 
from  its  upper  edge.  (See  Tyndall  on  Sound.) 

An  effect  just  opposite  this,  the  shortening  of  tall  flames, 
was  first  noticed  by  Mr.  Barrett  of  London,  in  1865.  He 
says  ("Chemical  News,  American 
Reprint,"  July,  1868),  "A  jet  of 
gas  issuing  from  a  V-shaped  orifice 
was  found  to  be  quite  insensible  to 
sound  until  the  flame  reached  a  height 
of  ten  or  twelve  inches  (see  Fig.  75)  ; 
and  then,  at  the  sound  of  certain  high 
tones,  the  flame  shortened,  and  spread 
out  into  a  fan-shape."  Another  flame 
he  thus  describes:  "So  sensitive  is 
this  flame,  that  even  a  chirp  made  at 
the  far  end  of  the  room  brings  it  down 
more  than  a  foot.  Like  a  living  be- 
ing, the  flame  trembles  and  cowers 
down  at  a  hiss  ;  it  crouches  and  shiv- 
ers as  if  in  agony  at  the  crisping  of 
this  metal  foil,  though  the  sound  is  so 
faint  as  scarcely  to  be  heard  ;  it  dances  in  tune  to  the  waltz 
played  by  this  musical  box  ;  and,  finally,  it  beats  time  to 
the  ticking  of  my  watch." 

Mr.  Barrett  also  suggests  that  these  flames  may  yet  be 
turned 'to  some  use,  and,  to  illustrate,  suggests  an  arrange- 
ment shown  in  Fig.  75. 

Near  the  tall  sensitive  flame  a,  stand  two  vertical  brass 
rods,  b  c.  Projecting  from  these  rods  are  two  metallic  rib- 
bons, made  of  layers  of  silver,  gold,  and  platinum  welded 
together.  The  ends  of  the  ribbons  are  about  half  an  inch 
apart.  By  heat  the  different  metals  expand  unequally,  and, 


Fig.  75. 


NATURAL  PHILOSOPHY.  167 

bending  the  ribbons,  bring  their  ends  together.  The  brass 
rods  are  connected  by  wires  with  an  electric  bell  at  a  distance. 
Now,  as  long  as  the  tall  flame  is  not  disturbed,  the 
metallic  ribbons  are  not  in  contact:  the  circuit  is  broken, 
and  the  bell  is  silent ;  but  at  the  sound  of  a  whistle  the 
flame  jumps  down,  warms  the  ribbons,  completes  the  electric 
circuit,  and  rings  the  distant  bell. 


SECTION  IV. 

REVIEW. 
I. —SUMMARY   OF  PRINCIPLES. 

Undulations  with  rates  between  16  per  second  and  38,000 
per  second  will  affect  the  ear  as  sound. 

Such  undulations  can  traverse  all  kinds  of  elastic  bodies, 
but  not  with  the  same  velocity. 

The  velocity  in  a  denser  medium  is  less  than  in  a  rarer 
one.  In  a  more  elastic  medium  it  is  greater  than  in  one  less 
elastic. 

The  laws  are  expressed  by  the  formula :  — 

V  = 

When  sound-waves  flow  against  an  obstacle,  they  are 
thrown  back,  or  reflected.  The  angle  of  reflection  equals 
the  angle  of  incidence. 

Any  sound  repeated  with  great  regularity  and  rapidity 
becomes  a  musical  tone. 

Tones  differ  in  pitch,  in  intensity,  and  in  quality,  or,  as 
the  French  call  it,  timbre. 

The  pitch  depends  upon  the  rate  of  the  waves. 

The  intensity  depends  upon  the  amplitude  of  the  waves. 

The  quality  depends  upon  the  form  of  the  waves. 

Waves  of  the  same  rate,  amplitude,  and  form  will  be 
recognized  as  the  same  sound,  in  whatever  way  they  may 
be  produced. 


168  NATURAL   PHILOSOPHY. 

II.— SUMMARY   OF  TOPICS. 

61.  Sound-waves.  —  Traverse     elastic     bodies.  —  With 
different   velocfty.  —  The   first    law.  —  The    second   law.  — 
Velocity  uniform  in  the  same  medium.  —  Application.  — The 
formula.  — Effect  of  temperature. 

62.  Reflection  of  sound.  —  The  law.  —  Explanation  of  the 
echo.  —  Multiple  echo. 

63.  Musical  sound.  — Continuous  tone  by  rapidly  repeated 
impulses. — The  siren.  —  Description   of  the   siren.  —  Ex- 
planation of  its  action. 

64.  Pitch   depends   on   rate.  —  Intervals. — The  diatonic 
scale. — English  and  French  standards  of  pitch. — Relative 
rates  for  the  eight  notes. — Absolute  rates.  —  Intensity. — 
Quality  defined.  —  Compound  tones.  —  Illustration.  —  Over- 
tones.—  Helmholtz'  theory  of  quality. 

.    65.  The  phonograph.  — To  record  the  voice.  —  To  repro- 
duce the  voice. 

66.  Stringed   instruments.  —  Pitch  varied   b}T  strings   of 
different  lengths. — Different  tensions. — Different  weights. 
—  Wind-instruments. 

67.  The  musical  flame. — Pitch  of  the  tone. — The  sensi- 
tive flame. 


NATURAL  PHILOSOPHY.  169 


CHAPTER   VII. 
ON  RADIANT  ENERGY:   LIGHT. 


SECTION    I. 
ON   TRANSMISSION. 

68.  RAYS  of  light  are  transmitted  through  some  media 
more  freely  than  through  others,  but  always  according  to  two 
laws :  — 

1st,  In  a  medium  of  uniform  density,  light  goes  in  straight 
lines  with  a  uniform  velocity. 

2d,  The  intensity  of  light  varies  inversely  as  the  square 
of  the  distance  from  its  source. 

The  art  of  Photometry  depends  upon  this  second  law.  (G. 
489,  491-493,  495  ;  A.  795,  803.) 

Wave-Front.  —  When  a  pebble  falls  into  quiet  water,  a 
wave  advances  outward  like  the  rim  of  an  expanding  wheel. 
The  outside  of  this  circular  wave  is  the  wave-front. 

When  a  gas-jet  is  lighted,  a  wave  darts  outward,  advancing 
in  ever}7  direction  like  the  surface  of  an  expanding  sphere. 
The  outside  of  this  spherical  wave  is  the  wave-front. 

The  outside  of  an  advancing  wave  of  any  kind  is  called 
the  WAVE-FRONT. 

Kays  of  Light.  —  A  single  line  of  light,  or,  more  accu- 
rately, the  path  of  a  single  point  in  the  wave-front,  is  called 
a  RAY  of  light.  But  a  ray  of  light  is  quite  too  delicate  a 
thing  to  be  seen.  The  smallest  portion  of  light  which  can 
be  separated  by  experiment  consists  of  many  rays.  A  col- 
lection of  parallel  rays  is  called  a  BEAM  of  light.  A  collec- 


170  NATURAL  PHILOSOPHY. 

tion  of  ra}Ts  which  diverge  from  a  point,  or  which  converge 
toward  a  point,  is  called  a  PENCIL  of  light. 

Kays  of  Liglit  are  transmitted.  —  Some  substances  per- 
mit light  to  pass  through  them  freely ;  they  are  said  to  be 
transparent.  Air  and  water  are  examples  of  transparent 
bodies.  Others,  such  as  iron  and  wood,  appear  to  forbid 
the  passage  of  light  through  them :  they  are  said  to  be 
opaque.  But  no  substance  will  transmit  all  the  light  which 
it  receives  ;  even  the  air  is  not  perfectly  transparent.  On 
the  other  hand,  no  substance  will  stop  all  the  light  which 
falls  upon  it;  even  gold,  when  a  very  thin  leaf  of  it  is  ex- 
amined, can  be  seen  to  transmit  light.  All  substances  are 
doubtless  able  to  transmit  light  in  some  degree. 

Liglit  moves  in  straight  Lines. — That  light  moves  in 
straight  lines,  is  shown  by  numerous  familiar  facts.  We  can 
not  see  through  a  crooked  tube,  simpl}'  because  light  can 
not  pursue  a  crooked  path.  And  again  :  who  has  not  seen 
the  sunlight  coming  through  the  shutters  of  a  half-darkened 
parlor,  spotting  the  opposite  wall  with  circles  of  light?  The 
sun,  the  hole  in  the  shutter,  and  the  spot  on  the  wall,  are 
always  in  the  same  straight  line.  Let  the  air  of  the  room  be 
sprinkled  with  dust,  and  the  paths  of  the  sunbeams  are  seen 
streaking  the  air  with  bars  of  light. 

With  uniform  Velocity.  —  Light  travels  through  space 
with  a  uniform  velocity  of  about  186,000  miles  a  second. 
This  number  has  been  found  by  observing  the  eclipses  of  one 
of  the  moons  of  Jupiter.  The  time  when  the  eclipse  should 
begin  can  be  calculated  by  an  astronomer  with  great  accu- 
rac}T.  But  it  is  found  that  when  the  earth  is  in  that  part 
of  its  orbit  nearest  to  Jupiter,  the  eclipse  begins  16  minutes 
and  36  seconds  sooner  than  it  appears  to  when  the  earth  is 
in  the  opposite  part  of  its  orbit.  It  must,  therefore,  take 
light  16  minutes  and  36  seconds  to  go  across  the  earth's 
orbit.  When  this  distance  is  known,  and  divided  by  the 
number  of  seconds,  the  velocity  of  light  is  found.  The  re- 
sult is  about  186,000  miles  a  second.  For  all  distances  on 


NATURAL  PHILOSOPHY. 


171 


Fig.  76. 


the  surface  of  the  earth,  the  passage  of  light  may  be  con- 
sidered instantaneous.  It  would  go  around  the  world  almost 
seven  times  in  a  single  second. 

The  Second  Law.  —  That  the  intensity  of  light  varies 
inversely  as  the  square  of  the  distance,  may  be  easily  proved 
by  experiment. 

A  square  piece  of  stiff  cardboard,  A  (Fig.  76),  is  placed 
in  front  of  another,  B,  very  much  larger.  If  now  a  candle- 
flame  be  placed  in  front 
of  the  small  card,  a 
shadow  will  be  cast 
upon  the  large  one* 
This  shadow  will  be 
larger  as  the  small  card 
is  moved  nearer  to  the 
flame  ;  it  will  be  small- 
er as  it  is  moved  the 
other  way.  The  figure 
is  intended  to  show  the  small  card  to  be  just  one-fourth  as  far 
from  the  flame  as  the  large  one.  In  this  case  the  shadow  will 
be  found  to  be  exactly  sixteen  times  as  large  as  the  card  in 
front  of  it.  Now,  the  same  amount  of  light  which  is  spread 
over  the  small  card  would,  if  it  could  go  on,  just  cover  the 
place  of  this  shadow.  But,  if  the  same  amount  of  light  is 
spread  over  sixteen  times  as  much  surface  in  one  case  as  in 
another,  it  can  be  only  one-sixteenth  as  intense.  At  four 
times  the  distance  from  the  luminous  bod}',  in  this  case,  the 
intensity  of  the  light  is  one-sixteenth  as  great.  At  three 
times  the  distance,  the  light  would,  in  the  same  way,  be 
found  to  be  one-ninth  as  intense.  In  other  words :  the  in- 
tensity of  light  varies  inversely  as  the  square  of  the  distance 
from  the  luminous  body. 

Photometry.  —  It  is  often  desirable  to  compare  the  illu- 
minating powers  of  different  flames.  ,  The  art  of  doing  this 
is  called  PHOTOMETRY.  The  simplest  method  is  to  place  the 
two  flames  at  such  distances  from  a  screen,  that  the  intensi- 


172  NATURAL    PHILOSOPHY. 

ties  of  the  light  they  shed  upon  it  shall  be  equal ;  the  illu- 
minating powers  of  the  flames  must  then  be  as  the  squares  of 
these  distances.  Suppose,  for  example,  that  we  wish  to  know 
how  many  times  more  light  one  candle  will  give  than  another 
of  inferior  quality.  Let  a  slender  rod  B  (Fig.  77)  be  put  just 
in  front  of  a  white  screen  A,  and  then  move  the  flames  to  such 
distances  that  the  two  shadows  of  the  rod,  falling  side  by  side 


Fig.  77. 

upon  the  screen,  shall  appear  to  be  of  equal  darkness.  The 
intensities  of  their  lights  on  the  screen  must  then  be  equal. 
Measure  the  distances  from  the  flames  to  the  screen :  the 
amounts  of  light  the}T  give  will  be  as  the  squares  of  their 
distances.  One  being  twice  as  far  away  as  the  other,  it  gives 
four  times  as  much  light. 

SECTION   II. 
ON    REFLECTION. 

69.  When  light  in  passing  through  one  medium  comes 
against  the  surface  of  another,  only  a  part 
will  enter ;  another  part  will  be  reflected, 
obeying  the  following  law  :  — 

The  angles  of  incidence  and  reflection 
must  be  equal,  and  in  the  same  plane.  (G. 
497;  A.  881,  882.) 

Reflection.  —  The  reflection  of  light  is 
in  all  respects  like  the  reflection  of  sound. 
The  same  terms  are  used  to  describe  it ; 
the  same  figure  may  be  reproduced  to  illustrate  it.     Thus  in 


NATURAL   PHILOSOPHY.  173 

Fig.  78,  the  line  I  A  ma}'  represent  a  beam  of  light  passing 
through  air,  and  striking  upon  the  surface  of  a  plate  of  glass 
at  A.  One  part  of  the  beam  will  enter  the  glass,  and  emerge 
again  on  the  other  side  ;  but  another  part  will  be  thrown 
back  into  the  air  in  the  direction  A  R.  The  beam  I  A  is 
the  incident  beam.  The  beam  A  R  is  the  reflected  beam. 
The  point  A  is  the  point  of  incidence. 

The  Law  of  Reflection.  —  The  reflection  of  light  is  also 
governed  by  the  same  law  as  the  reflection  of  sound.  The 
angle  I  A  P  (Fig.  78)  is  the  angle  of  incidence.  The  angle 
P  A  R  is  the  angle  of  reflection.  These  two  angles  must 
be  equal. 

Illustrations.  —  How  various  and  beautiful  are  the  phe- 
nomena which  this  principle  of  reflection  explains  !  The 
sky,  with  all  its  floating  clouds  or  shining  stars,  is  painted 
in  ever}'  pool  of  water,  because  the  light  from  them,  falling 
on  the  surface  of  the  water,  is  reflected  to  our  eyes.  Rocks, 
and  shrubbery,  and  dwellings  along  the  shore,  are  pictured 
in  the  quiet  waters  of  the  lake,  with  skill  exceeding  that  of 
any  human  artist. 

Vision  is  produced  by  reflected  light.  How  seldom  do  we 
receive  the  direct  rays  of  the  sun  into  the  eye  !  How  rarely, 
indeed,  do  we  look  directly  upon  any  luminous  body !  But 
in  all  other  cases  we  see  objects  only  by  reflected  light. 
The  sunbeams  fall  upon  all  objects  exposed  to  them,  and, 
bounding  from  their  surfaces,  enter  the  eye  ;  and  we  see  them 
in  the  direction  from  which  the  reflected  rays  have  come. 

70.  The  effects  of  mirrors  are  explained  by  reference  to 
the  law  of  reflection. 

Rays  of  light  reflected  by  a  plane  mirror  have  the  same 
relation  to  each  other  as  before  reflection  ; 

But  the  effect  of  a  concave  mirror  is  to  collect  the  rays  of 
light  which  are  reflected  by  it ; 

While  a  convex  mirror  always  separates  the  rays  which  it 
reflects.  (G.  506.) 


174  NATURAL  PHILOSOPHY. 

Mirrors.  —  Any  surface  smoothly  polished,  that  will  reflect 
nearly  all  the  light  which  falls  upon  it,  is  called  a  MIRROR. 
The  smooth  surface  of  quiet  water  is  a  very  perfect  mirror. 
Artificial  mirrors  are  generally  made  of  metal  or  of  glass. 
If  made  of  glass,  a  thin  film  of  mercury  is  spread  over  one 
side,  and  the  smooth  surface  of  this  metallic  coating  is  really 
the  reflecting  surface.  Mirrors  are  either  plane  or  curved. 
Of  the  curved  mirrors  there  are  two  varieties,  —  the  concave 
and  the  convex. 

The  effect  of  Plane  Mirrors.  —  The  rays  of  light  which 
fall  upon  a  mirror  may  be  parallel,  or  converging,  or  diver- 
ging, but  can  have  no  other  relation.  Now,  let  the  mirror 
be  represented  by  the  straight  line  A  B  (Fig.  79),  and  sup- 
pose, first,  that  it  receive  two  parallel  rays  represented  by 

the  lines  a  c  and  b  d.  At  the 
point  of  incidence,  c,  erect  a 
perpendicular  to  the  surface 
A  B.  The  angle  a  eg  will  be 
the  angle  of  incidence.  Then 
draw  the  line  c/,  so  as  to 

make  the  angle  of  reflection,  g  c  f,  equal  to  the  angle  of 
incidence,  and  cf  must  be  the  direction  of  the  ray  reflected 
from  the  point  c.  Again :  at  the  point  of  incidence,  d,  erect 
a  perpendicular,  and  draw  the  line  d  e,  making  the  angle  of 
reflection  equal  to  the  angle  of  incidence,  and  this  line  must 
represent  the  ray  reflected  from 
the  point  d.  It  will  be  found 
that  the  reflected  rays,  c/and 
d  e,  will  be  parallel. 

Suppose,  second,  that  two 
ra}*s,  a  c  and  6  d  (Fig.  80), 
are  converging,  and  strike  the 
mirror  at  the  points  c  and  d. 

By  making  the  angles  of  incidence  and  reflection  equal,  ex- 
actly as  it  was  done  in  the  preceding  case,  we  find  that  the 
reflected  rays  will  take  the  directions  c  e  and  d  e?  converging 
to  the  ppint  e. 


NATURAL  PHILOSOPHY. 


175 


Fig.  81. 


Suppose,  third,  that  the  ra}rs  are  diverging.  Represent 
them  by  lines  a  c  and  a  d  (Fig.  81).  Erect  the  perpendicu- 
lars, and  construct  the  angles  of  incidence  and  reflection 
equal,  and  the  directions  of  the  reflected  rays  will  be  ce  and 
d  /,  diverging  from  each  other. 

In  each  of  these  three  cases,  the  reflected  rays  have  the 
same  relation  as  the  incident 
rays. 

The  effect  of  Concave 
Mirrors.  —  We  will  notice 
only  those  concave  mirrors 
whose  surfaces  are  spherical. 
If  we  know  the  direction  of 
the  incident  ra3"s,  we  can  find 

the  direction  of  the  reflected 

,  .  ,       „ 

rays  by  making  the  angle  of 

reflection  equal  to  the  angle  of  incidence.     To  construct  the 

angle  of  incidence,  we 
must,  as  in  the  plane  mir- 
ror, erect  a  perpendicular 
to  the  concave  surface  at 
the  point  of  incidence  ; 
and  all  difficulty  disap- 
pears when  we  remember 
that  a  perpendicular  to 
any  spherical  surface  is 
the  radius  of  the  sphere. 
In  Fig.  82,  MN  repre- 
sents a  section  of  a  con- 
cave  mirror.  The  point 
C  represents  the  center  of  curvature,  that  is,  the  center  of 
the  hollow  sphere  of  whose  concave  surface  the  mirror  is  a 
part.  Now,  if  E  A  and  D  B  represent  two  parallel  inci- 
dent rays,  and  we  wish  to  find  the  direction  they  take  after 
reflection,  we  may  draw  the  radii  C  A  and  C  B,  making  the 
angles  of  incidence  E  A  C  and  D  B  C,  and  then  draw  the 


"EM  o* 


176  NATURAL  PHILOSOPHY. 

lines  A  F  and  B  F,  so  as  to  make  the  angles  of  reflection 
equal  to  these.  B}'  so  doing,  we  find  that  the  reflected  rajs 
converge,  and  cross  each  other  at  the  point  F. 

In  Fig.  83,  the  lines  E  A  and  D  B  represent  converging 

rays.  By  construct- 
ing the  angles  of  in- 
cidence and  reflec- 
tion in  the  same  wa}T 
as  before,  we  find 
that  the  reflected 
ra}Ts  cross  each  other 
at  the  point  F,  con- 
verging faster  after 
reflection  than  be- 
fore. 

In  the  same  figure, 

F  A  and  F  B  may  represent  diverging  rays,  striking  the  mir- 
ror at  the  points  A  and  B.  By  constructing  the  angles* of 
incidence  and  reflection  equal,  we  find  the  reflected  rays  tak- 
ing the  directions  A  E  and  B  D,  diverging  less  after  reflec- 
tion than  before. 

Now,  since  parallel  rays  are  made  converging,  and  con- 
verging rays  are  made  more  converging,  while  diverging  rays 
are  made  to  diverge  less,  we  may  sa}'  that  the  general  effect 
of  a  concave  mirror  is  to  collect  rays  of  light. 

Foci.  —  A  focus  is  any  point  where  rays  of  light  cross,  or 
appear  to  cross,  after  reflection.  The  points  F,  in  Figs.  82 
and  83,  are  foci.  The  axis  of  a  mirror  is  a  straight  line 
drawn  through  the  center  of  curvature  and  the  middle  point 
of  the  mirror. 

In  Fig.  84,  the  line  C  A  is  the  axis  of  the  mirror  M  N, 
whose  center  of  curvature  is  at  C.  The  focus  of  rays  that 
are  parallel  to  the  axis,  and  fall  upon  the  mirror  near  its 
middle  point,  is  called  the  PRINCIPAL  Focus.  If  the  rays 
B  E  and  D  H  (Fig.  84)  are  near  and  parallel  to  the  axis 
C  A,  they  will,  after  reflection,  cross  each  other  at  the  point 


NATURAL   PHILOSOPHY. 


177 


F,  and  this  point  is  the  principal  focus  of  the  mirror.  The 
principal  focus  is  on  the  axis,  half  way  between  the  center  of 
curvature  and  the  mir- 
ror. 

The  effect  of  Con- 
vex  Mirrors.  —  In 
Fig.  85,  a  convex 
mirror  is  represented 
by  M  N,  its  center  of 
curvature  by  the  point 
C.  Two  parallel  rays 
of  light,  E  A  and  D 
B,  strike  the  mirror  at 
the  points  A  and  B. 
To  construct  the  angles  of  incidence,  we  must  erect  per- 
pendiculars to  the  surface  at  these  points.  The  perpendic- 
ulars are  the  radii,  C  A  and  C  B,  extended  beyond  the  convex 


Fig.  84. 


Fig.  85. 


surface  of  the  mirror.  By  making  the  angles  of  reflection 
equal  to  the  angles  of  incidence,  the  reflected  rays  are  found 
to  take  the  directions  A  F  and  B  H.  We  notice  that  parallel 
rays  are  rendered  diverging. 


178 


NATURAL   PHILOSOPHY. 


So  we  might  show  that  diverging  rays  would  be  made  more 
diverging,  and  that  converging  ra}'s  would  be  made  to  con- 
verge less.  We  say,  therefore,  that  the  general  effect  of  a 
convex  mirror  is  to  separate  rays  of  light. 

71.  When  the  light  reflected  from  a  mirror  enters  the  eye, 
we  see  an  image  of  the  object  from  which  the  light  proceeds. 

The  image  of  an}r  point  will  always  be  found  where  the 
rays  of  light  which  go  from  that  point  either  meet,  or  appear 
to  meet,  after  reflection. 

The  image  formed  by  a  plane  mirror  is  always  as  far  be- 
hind the  mirror  as  the  object  is  in  front  of  it ;  the  same 
size  as  the  object,  and  erect.  (G.  501-503  ;  A.  883-885.) 

Images  by  Reflection.  —  When  an  object,  a  lighted 
candle  for  example,  stands  before  a  looking-glass  (Fig.  86), 

numberless  ra}'s 
of  light  from 
every  point  of  it 
fall  upon  the  mir- 
ror. These  rays 
are  reflected,  and 
man}'  of  them  are 
thrown  into  the 
e}re.  Those  wrhich 
enter  the  eye 
cause  us  to  see 
the  image  in  the 
glass. 

The  Image  of  a  point.  —  Now,  if  the  rays  of  light, 
which  form  the  image  in  the  glass,  were  visible,  the  person 
would  be  able  to  trace  them  back  from  the  eye,  converging 
toward  the  points  on  the  glass  from  which  they  are  reflected, 
and  they  would  appear  as  if  they  came  from  points  in  the 
image  behind  the  glass. 

This  will  be  better  understood  by  means  of  Fig.  87.  Let 
M  N  represent  a  plane  mirror.  From  the  point  A,  number- 


Fig.  86. 


NATUBAL  PHILOSOPHY. 


179 


Fig.  87. 


less  rays  fall  upon  the  mirror,  some  of  which,  after  reflection, 

will  enter  the  e}'e  supposed 

to  be  at  O.     Two  of  these 

ra}*s  are  represented  in  the 

figure.     The  e}'e  will  receive 

these  rays  as  if  they  came 

from   the  point  <x,  and  this 

point  a  is  the  image  of  the 

point  A,  from  which  the  rays 

proceed. 

Images  by  Plane  Mir- 
rors. — We  are  now  prepared 

to  see   how  looking-glasses 

make  such  perfect  images  of 

all  objects   placed   in  front 

of  them.     Suppose  an  arrow,   A  B,  placed  before  a  mirror 

(Fig.    88).     Let   us   construct  its  image.     From   the   vast 

number  of  rays  which  go  from  A  to  the  glass,    select  two 

which  fall  upon  it  very  near  together,  at  /and  g.  By  mak- 
ing the  angles  of  reflection  equal 
to  the  angles  of  incidence,  we 
find  the  reflected  rays  taking  the 
directions/  P  and  g  O.  Now,  if 
the  eye  be  placed  at  E,  it  will  re- 
ceive these  reflected  rays  as  if 
they  came  from  the  point  a. 
Again,  select  two  rays,  which, 
going  from  the  other  end  of  the 
arrow  B,  strike  the  mirror  at 
points  near  together  at  c  and  d, 
so  that  after  reflection  they  can 
enter  the  same  eye  at  E.  These 
Fig.  88.  ra^g  w-jj  appear  to  have  come 

from  b.  From  all  points  between  A  and  B,  rays  of  light 
will  go  to  the  mirror ;  and,  being  reflected,  will  enter  the  eye 
at  E,  and  appear  to  have  come  from  points  between  a  and 


180  NATURAL  PHILOSOPHY. 

b.  The  image  of  the  arrow,  A  B,  will  thus  be  seen  at  a  b. 
We  ma}-  describe  this  image  thus  :  The  image  made  by  a  plane 
mirror  is  always  behind  the  mirror,  just  as  far  as  the  object 
is  in  front  of  it,  of  the  same  size  as  the  object,  and  erect. 

72.  If  an  object  be  placed  in  front  of  a  concave  mirror, 
the  position  and  size  of  the  image  will  depend  upon  the  dis- 
tance of  the  object  from  the  mirror.  We  will  notice  three 
well-marked  cases :  — 

1st,  When  the  object  is  beyond  the  center  of  curvature. 

2d,  When  the  object  is  between  the  center  of  curvature 
and  the  principal  focus. 

3d,  When  the  object  is  between  the  principal  focus  and 
the  mirror.  (G.  519-521.) 

Images  are  formed.  —  The  brilliant  inner  surface  of 
a  silver  spoon  shows  the  image  of  a  person  who  looks  upon 
it,  but  it  will  be  curiously  different  from  his  image  seen  in  a 
looking-glass.  It  is  very  small ;  it  is  inverted  ;  and,  more- 
over, by  careful  attention,  the  person  sees  his  picture  stand- 
ing in  the  air  between  himself  and  the  surface  of  the  spoon. 
Nor  is  this  all :  the  picture  in  the  air  will  grow  larger  or 
smaller,  or  it  ma}'  disappear  altogether,  as  the  spoon  is 
moved  toward  or  from  the  face  of  the  observer. 

If  a  spherical  concave  mirror  of  small  curvature  be  at 
hand,  a  beautiful  experiment  will  illustrate  its  power  to  form 
images.  Let  a  lighted  candle  be  placed  in  front  of  a  con- 
cave mirror.  The  mirror  will  receive  the  light,  and  reflect 
the  rays  upon  the  wall  above  the  window  ;  and,  if  its  distance 
from  the  candle  is  just  right,  a  fine  image,  much  larger  than 
the  candle,  and  with  the  flame  downward,  will  be  seen  upon 
the  wall  or  screen  (Fig.  89). 

The  Images  of  Points.  —  How  is  this  beautiful  effect 
produced?  Can  we  find  the  images  of  points  of  the  object 
by  tracing  the  reflected  rays  which  produce  them  ?  Let  M  N 
(Fig.  90)  represent  a  section  of  the  concave  mirror,  and 
suppose  an  arrow,  A  B,  in  front  of  it.  Select  two  rays  of 


NATURAL   PHILOSOPHY. 


181 


light  which,  going  from  the  point  A,  fall  upon  the  mirror  at 
D  and  E.     After  reflection  they  will  cross  each  other  at  A'. 


Fig.  89. 

Again  select  two  rays,  which,  going  from  the  point  B,  fall 
upon  the  mirror  at  the  points  H  and  F.  After  reflection 
they  will  cross  each  other  at  B'.  Other  points  in  the  object 


Jb'ig. 

will  send  rays  to  the  mirror,  which,  after  reflection,  will 
cross  each  other  at  points  between  A'  and  B'.  In  this  way 
a  large  and  inverted  image  is  made  in  the  air  at  A'  B'. 


182  NATURAL  PHILOSOPHY. 

Case  1:  Object  beyond  the  Center.  — Let  M  N  (Fig. 
91)  represent  a  section  of  the  concave  mirror,  whose  center 
of  curvature  is  C,  and  whose  principal  focus  is  F.  Suppose 
an  arrow,  A  B,  to  be  put  in  front  of  the  mirror,  be3'ond  the 
center  of  curvature.  A  perfect  image  of  the  arrow  will 
thus  be  formed  at  A'  B'.  In  this  case  we  observe  that  the 
image  is  between  the  center  of  curvature  and  the  principal 
focus,  inverted,  and  smaller  than  the  object. 


Fig.  91. 

This  case  was  illustrated  by  the  experiment  with  the 
silver  spoon. 

Case  2:  The  Object  between  the  Center  and  Focus. 

—  Now  let  us  suppose  that  in  this  same  Fig.  91  an  arrow 
B'  A',  with  its  head  pointing  downward,  is  placed  between 
the  center  of  curvature  and  the  principal  focus.  The  image 
of  the  arrow  will  be  formed  at  A  B.  In  this  case,  we  ob- 
serve that  the  image  will  be  beyond  the  center  of  curvature, 
inverted,  and  enlarged. 

This  case  was  illustrated  by  the  experiment  with  the 
candle,  Fig.  89. 

Object  nearer  to  the  Focus.  —  When  the  object  is 
gradually  moved  from  the  center  toward  the  focus,  the  im- 
age will  rapidly  move  farther  and  farther  away,  until,  when 
the  object  has  reached  the  focus,  the  image  will  be  at  an 
infinite  distance  in  front  of  the  mirror,  and  of  course  in- 
visible. But  let  the  object  be  carried  a  little  farther,  so  as 
to  be  between  the  focus  and  the  mirror,  and  the  image 
suddenl}7  leaps  from  its  distant  place  in  front  of  the  mirror, 
to  a  position  behind  it- 


KATITRAL  PHILOSOPHY . 


188 


Case  3:  The  Object  between  the  Focus  and  the 
Mirror.  —  To  illustrate  the 
formation  of  this  image  behind 
the  mirror,  let  A  B  (Fig.  92) 
represent  an  object  between 
the  focus  F,  and  the  mirror 
M  M'.  Tracing  the  rays  from 
A  and  from  B,  we  find  that 
after  reflection  they  enter  the 
eye  at  E,  and  appear  as  if  they 
came  from  a  and  b.  In  this 
case  we  observe  that  the  image 


Fig.  92. 


is  behind  the  mirror,  erect,  and  larger  than  the  object. 

73.  The   images   formed   by  convex   mirrors   are   always 
behind  the  mirror,  erect,  and  smaller  than  the  object. 

Images  by  Convex  Mirrors.  —  The  convex  surface  of  a 
silver  spoon  will  serve,  in  a  homely  way,  to  illustrate  the 
effects  of  a  convex  mirror.  A  person 
looking  upon  it  will  see  his  own  image, 
apparently  in  the  metal  of  the  spoon, 
erect,  but  very  small.  The  diagram 
(Fig.  93)  shows  how  these  images  are 
formed. 

74.  The  law  of  reflection  applies  to 
rough  surfaces  as  well  as  to  mirrors. 

Reflection  from  Rough  Surfaces. 

—  Reflection  from  a  rough  surface  is 
represented  in  Fig.  94.  The  light  is 
scattered  in  all  directions.  Yet  the  law  of  reflection  is  not 
transgressed.  Every  ray  must  be  thrown  in  such  a  direction 
that  the  angle  of  reflection  is  equal  to  the  angle  of  inci- 
dence. But  on  a  rough  surface,  like  that  seen  in  Fig.  94, 
the  reflecting  points  are  not  in  regular  order,  and  for  this 
reason  the  reflected  rays  are  not. 


Fig.  93. 


184 


NATURAL  PHILOSOPHY. 


Fig.  94. 


SECTION  III. 

ON   REFRACTION. 

75.  When  light  passes   from  one   medium   into   another 

of  different  density,  it  is 
refracted,  obeying  the  fol- 
lowing laws  :  — 

1st,  In  passing  into  a 
denser  medium,  light  is 
bent  toward  a  perpendicu- 
lar to  the  surface  at  the 
point  of  incidence. 

2d,    In   passing   into    a 
rarer  medium,  light  is  bent 
from  the  perpendicular.     (G.  523-526  ;  A.  807.) 

The  Experiment.  — 
Through  a  small  opening 
in  the  shutter  of  a  dark- 
ened room,  let  a  beam  of 
sunlight  enter,  and  fall 
obliquety  upon  the  surface 
of  water  held  in  a  glass 
vessel  (Fig.  95).  If  the 
water  has  been  made  tur- 
bid by  the  addition  of  a 
little  soap,  and  the  air 
above  it  misty  by  sprink- 
ling into  it  the  dust  of  a 
chalk-brush,  the  beam  of 
light  will  be  distinctly 
seen  in  both,  absolutely 
straight  except  at  the  sur- 
face of  the  water,  where 
it  will  be  very  considerably  bent. 


Fig.  95. 


r 


NATURAL  PHILOSOPHY. 


185 


Definition.  —  This   change   in  the   direction  of  a  wave 
on  entering  a  second  medium  is  called  REFRACTION. 

The  First  Law  of  Refraction.  —  If  now  a  perpen- 
dicular, F  E,  be  erected  to  the  refracting  surface  at  the  point 
of  incidence,  B  (Fig.  96),  we  see  that 
the  raj's  A  B,  instead  of  moving  in  a 
straight  line  onward  to  C,  will  be  bent 
toward  the  perpendicular.  Water  is 
denser  than  air.  In  going  from  the 
rarer  to  the  denser  medium,  the  light  is 
bent  toward  the  perpendicular. 

The  Second  Law  of  Refraction. — 
Let  us  suppose  that  D  B  represents  a 
beam  of  light  going  from  the  water 
into  the  air  at  B  ;  it  will  take  the  direc- 
tion B  A,  instead  of  going  on  in  a  straight  line  toward  P, 
being  bent  from  the  perpendicular  F  E.  In  passing  from 
the  denser  medium  into  the  rarer,  the  light  is  bent  from  the 
perpendicular. 

Many  phenomena  in  nature  may  be  explained  by  reference 

to  these  principles. 
When,  for  example,  an 
oar  is  dipped  into  clear 
and  quiet  water,  it  ap- 
pears broken  at  the  sur- 
face (Fig.  97).  The 
light  comes  to  the  e}'e 
from  all  points  of  the 
oar.  From  that  part 
which  is  above  water 


it  comes  in  straight  lines 
through  the  air,  but 
from  the  part  under  the  water  the  light  coming  up  into  the 
air  is  bent  at  the  surface.  The  eye  which  receives  these  bent 
rays  traces  them  back  in  straight  lines;  and  the  oar,  from 
which  they  come,  is  thus  made  to  appear  to  be  where  it  really 
is  not 


Pig.  97. 


186  NATURAL   PHILOSOPHY. 

76.  Some  substances  refract  light  more  than  others.  Their 
relative  refracting  powers  are  indicated  by  certain  numbers, 
which  are  called  INDICES  OF  REFRACTION. 

The  Index  of  Refraction.  —  We  may  best  explain 
the  meaning  of  this  term  by  means  of  the  following  diagram. 
Suppose  a  small  beam  of  light,  R  I  (Fig.  98) ,  to  be  passing 

from  air  into  water.  It  will 
be  bent  at  I,  and  go  on  in 
the  direction  of  I  S.  Now, 
with  the  point  I  as  a  cen- 
ter, and  with  an}T  conven- 
ient radius,  describe  a  cir- 
cumference. Let  a  perpen- 
dicular, P  I,  be  erected  to 
the  surface  of  the  water  at 
the  point  I,  and  from  the 
points  S  and  o  let  lines  be 
drawn  perpendicular  to  P  I. 
The  perpendicular  from  o  is 

the  sine  of  the  angle  of  incidence,  and  that  from  S  is  the 
sine  of  the  angle  of  refraction.  If  now  we  measure  the 
lines  o  t  and  P  S,  and  divide  the  length  of  o  t  by  that  of 
P  S,  we  will  obtain  a  quotient  which  is  called  the  INDEX  OF 
REFRACTION. 

The   Law.  —  Now,  R  I  might  make  a  larger  angle  of  in- 
cidence or  a  smaller  one,  i.e.,  the  light  might  enter  more  or 
(ess  obliquely  into  the  water,  but  still  the  quotient  found  by 
dividing  the  sine  of  the  angle  of  incidence  by  the  sine  of  the 
angle  of  refraction  would  be  the  same, 
sin.  I_ 
sin.  R 

For  the  same  media  the  index  of  refraction  is  a  constant 
quantity. 

The  Index  varies  with  the  Media.  —  In  passing  from 
air  into  glass,  the  light  is  bent  more  than  when  passing  into 
water.  Hence  the  index  of  refraction  is  larger. 


NATUEAL   PHILOSOPHY. 


187 


The  larger  the  index  of  refraction,  the  greater  the  refract- 
ing power  of  the  substance. 

For  water,  the  index  of  refraction  is  always  1.336;  for 
crown-glass,  the  index  is  1.58  ;  for  the  bisulphide  of  carbon, 
it  is  1.673. 

77.  The  effects  of  lenses  are  explained  by  the  principles 
of  refraction. 

A  convex  lens  collects  the  rays  of  light  which  pass 
through  it. 

A  concave  lens  separates  the  rays  which  pass  through  it. 
(G.  540,  541,  544.) 

Lenses.  —  A  lens  is  a  transparent  body  bounded  by 
surfaces,  one  at  least  of  which  is  curved.  Six  different 
varieties  are  used  in  the  arts.  They  are  usually  made 
of  glass,  and  their  shapes  are  represented  by  sections  in 
Fig.  99 


Pig.  99. 


The  double  convex  lens,  A,  is  bounded  by  two  convex 
surfaces. 

The  plano-convex,  B,  is  bounded  by  surfaces,  one  of  which 
is  convex  and  the  other  plane. 

The  converging  concavo-convex,  C,  has  one  surface  convex 
and  the  other  concave,  the  convexit}^  being  greater  than  the 
concavity. 

The  double  concave  lens,  D,  has  two  concave  surfaces. 

The  plano-concave  lens,  E,  has  one  surface  concave  and 
the  other  plane. 

The  diverging  concavo-convex  lens,  F,  has  one  surface 
convex  and  the  other  concave,  the  convex  surface  being  less 
curved  than  the  concave  surface. 


188  NATURAL  PHILOSOPHY. 

The  first  three  of  these  varieties,  A,  B,  C,  are  convex 
lenses ;  the  others,  D,  E,  F,  are  concave  lenses. 

Effect  of  Convex  Lenses.  —  If  a  double  convex  lens  is 
held  in  the  path  of  a  sunbeam,  especially  in  a  darkened 
room,  the  rays  will  not  come  out  of  it  parallel :  they  will  be 
so  bent  as  to  all  come  to  one  point,  —  the  principal  focus  of 
the  lens,  as  we  are  shown  by  Fig.  100. 

We   may  suppose  the  rays   to  go  from  the  focus  to   the 


Pig.  100. 

lens :  these  ra}Ts  (FA,  Fig.  100)  are  diverging,  and,  as  the 
figure  represents  them,  they  will  be  parallel  after  going 
through  the  lens. 

But  diverging  rays  are  not  always  made  parallel ;  indeed, 
they  will  not  be  unless  they  start  from  the  principal  focus. 
If  they  start  from  a  point  between  the  focus  and  the  lens, 
they  will  diverge  after  going  through,  but  the  divergence  will 
be  less  than  before.  On  the  other  hand,  if  the  rays  start 
from  a  point  farther  than  the  focus  from  the  lens,  they  will 
be  converging  after  refraction.  This  case  is  beautifully 
shown  in  Fig.  101. 

We  should  find,  by  experiment,  that  in  all  cases  the  rays 
after  refraction  will  be  nearer  to  each  other  than  before.  The 
general  effect  of  the  convex  lens  is  to  collect  rays  of  light. 

The  plano-convex  lens  and  the  converging  meniscus  (C, 
Fig.  99)  will  have  the  same  effect,  but  in  a  less  degree. 

Foci.  —  The  point  F  in  Fig.  100  is  the  principal  focus  of 
the  lens :  it  is  the  focus  of  rays  which  are  parallel  to  the 


NATURAL  PHILOSOPHY.  189 

axis.  The  distance  of  this  point  from  the  lens  will  depend 
upon  the  curvature  of  the  lens,  and  upon  the  index  of  re- 
fraction. If  the  two  surfaces  of  the  lens  are  equally 
curved,  and  it  be  made  of  glass  whose  index  of  refrac- 


Fig.  101. 

tion  is  1.5,  then  the  principal  focus  will  be  at  the  center  of 
curvature. 

The  points  S  and  S'  in  Fig.  101  are  conjugate  foci.  They 
are  so  related  that  the  light  radiating  from  either  one  will  be 
collected  into  the  other. 

Effect  of  Concave  Lenses.  —  The  rays  after  passing 
through  a  concave  lens  are  separated  instead  of  being 
collected. 

This  effect  is  well  shown  in  Fig.  102,  which  represents  a 


Fig.  102. 


double-concave  lens  refracting  parallel  rays  of  light.  They 
are  supposed  to  enter  the  lens  on  the  side  F,  parallel  to 
each  other,  but  on  coming  out  on  the  other  side  they  are 


190  NATURAL   PHILOSOPHY. 

diverging.  Diverging  rays  are  made  more  diverging,  while 
converging  rays  are  made  less  converging.  In  all  cases, 
rays  refracted  by  a  double-concave  lens  are  separated. 

The  plano-concave  lens  and  the  diverging  concavo-convex 
lens  have  the  same  effect,  but  in  a  less  degree. 

78.  If  an  object  be  placed  in  front  of  a  convex  lens,  an 
image  of  it  will  be  formed  on  the  other  side  of  the  lens. 
To  explain  this,  remember  that  the  image  of  an}7  point  wffl 
be  made  where  rays  of  light  going  from  it  either  meet,  or 
appear  to  meet,  after  refraction. 

Images  are  formed. — If  a  convex  spectacle-glass  is  held 
in  front  of  a  window,  at  considerable  distance,  and  a  sheet 
of  white  paper  is  put  in  front  of  it,  the  light  from  the  window 
will  go  through  the  glass,  and  fall  upon  the  paper.  If  the 
distance  from  the  glass  to  the  paper  be  just  right,  a  very 
small  but  very  perfect  image  or  picture  of  the  window  will 
be  seen  upon  it. 


Pig.  103. 

If  a  good  double  convex  lens,  three  or  four  inches  in 
diameter,  be  at  hand,  a  very  beautiful  experiment  may  be 
made.  Through  an  opening  in  a  shutter  of  a  darkened 
room,  admit  a  beam  of  sunlight.  Into  this  beam  put  any 
small,  transparent  object,  it  may  be  a  picture  painted  on 
glass,  or,  quite  as  well,  a  wing  of  the  dragon-fly,  or  a  deli- 
cate flower.  If  now  the  lens  be  moved  back  and  forth  in 
front  of  this  object,  until  just  the  right  distance  is  found,  a 


NATURAL   PHILOSOPHY.  191 

very  large  and  perfect  image  will  be  seen  inverted  upon  th« 
opposite  wall  of  the  room.  (Fig.  103.) 

Explanation.  —  Now  let  us  see  how  these  beautiful 
effects  are  produced. 

Suppose  an  arrow  N  S,  (Fig.  104),  placed  at  some  dis. 
tance  in  front  of  a  convex  lens,  M,  whose  centers  of  curva- 
ture are  /  and  f.  Two  rays  of  light  from  the  point  N, 
passing  through 
the  lens,  will  be 
refracted  so  as  to 
cross  each  other 
at  the  point  n. 
This  point,  where 
rays  of  light  meet 
after  refraction ,  is  Flg*  1  °4' 

the  image  of  the  point  N,  from  which  they  came.  The  rays 
from  the  point  S  of  the  object,  after  refraction,  cross  each 
other  at  s,  and  form  an  image  there.  From  points  between 
N  and  S,  rays  of  light  going  through  the  lens  will  be  col- 
lected on  corresponding  points  between  n  and  s,  and  thus 
a  perfect  image  will  be  made  inverted  at  n  s. 

In  this  way  it  is  eas}*,  by  a  diagram,  to  illustrate  the 
formation  of  all  images  by  lenses. 

79.  The  place  and  size  of  the  image  will  depend  on  the 
distance  of  the  object  from  the  lens.  Four  typical  cases 
may  be  studied  :  — 

1st,  The  object  is  placed  at  twice  the  focal  distance  from 
the  lens. 

2d,  The  object  is  more  than  twice  the  focal  distance  from 
the  lens. 

3d,  The  object  is  beyond  the  focus,  but  less  than  twice  the 
focal  distance. 

4th,  The  object  is  at  less  than  the  focal  distance. 

Case  1:   The  Object  twice  the   Focal   Distance. — 

Suppose  the  lens  to  be  one  whose  focus  is  at  the  center  of 


192  NATURAL   PHILOSOPHY. 

curvature,  and  that  the  object  is  just  twice  that  distance 
from  the  lens,  as  shown  by  the  arrow  N  S  (Fig.  105).  Two 
rays  of  light  from  the  top  of  the  arrow  go  through  the  lens, 
bending  according  to  the  laws  of  refraction,  and  cross  each 

other  at  the  point 
n.  Two  rays  from 
the  bottom  of  the 
arrow  go  through 
the  lens,  and  cross 
each  other  at  the 
Fig'105-  points.  Join  the 

points  n  and  s,  and  n  s  represents  the  image  that  is  formed. 
This  image  will  be  at  twice  the  focal  distance  on  the  other  side 
of  the  lens,  of  the  same  size  as  the  object,  and  inverted. 

Case  2:  The  Object  farther  away.  —  This  case  is  rep- 
resented by  Figs.  103  and  104.  Suppose  that  in  front  of 
the  lens  M,  an  arrow,  with  its  head  downward,  represented 
by  n  s,  is  placed  at  more  than  twice  the  focal  distance  from 
the  lens.  Two  rays  from  the  arrow-head,  after  refraction, 
will  be  found  to  cross  each  other  at  N  ;  two  ra}'s  from  s  will, 
after  refraction,  cross  each  other  at  S.  The  image  N  S  is 
on  the  other  side  of  the  lens,  at  a  less  distance,  smaller  than 
the  object,  and  inverted. 

Case  3 :  The  Object  at  a  less  Distance.  —  If,  in  Fig. 
104,  we  suppose  N  8  to  represent  the  object,  outside  the 
focus,  but  at  less  than  twice  the  focal  distance,  its  image  will 
be  fc  ind  at  n  s.  In  this  case  the  image  will  be  at  a  greater 
distance  on  the  other  side  of  the  lens,  larger  than  the  object, 
and  inverted.  N 

Case  4:  The  Object  between  the  Focus  and  the 
Lens.  —  One  more  case  remains  to  be  considered.  Suppose 
the  object  to  be  between  the  focus  and  the  lens.  Let  M  N 
(Fig.  106)  represent  a  lens  whose  focus  is  at  C,  and  let  the 
object  A  B  be  placed  between  this  point  and  the  lens.  An 
attentive  examination  of  the  figure  shows  that  the  ra}'s  of 
light  from  the  point  A  are  diverging  after  refraction.  And, 


NATURAL   PHILOSOPHY. 


193 


since  they  can  never  meet,  it  is  clear  that  no  image  can  be 
formed  on  that  side  of  the  lens ;  but  if  an  eye  at  E  receive 
these  rays  they  will 
produce  the  same  ef- 
fect as  if  they  came 
from  A'.  In  like  man- 
ner, the  rays  from  B, 
entering  the  eye  at 
E,  will  seem  to  have 
come  from  B'.  Hence  Fig.  106. 

an  image  will  seem  to  be  formed  at  A'  B'.  This  image  will 
be  on  the  same  side  of  the  lens  as  the  object,  erect,  and  larger 
than  the  object. 


Fig.  107. 


80.  Images  are  also  formed  by  concave  lenses.     They  are 
on  the  same  side  as  the  object,  smaller,  and  erect. 

A 


Fig.  108. 

Image  by   Concave   Lens.  —  Suppose  an  object,  A  B 
(Figs.  107  and  108),  in  front  of  a  concave  lens  M  N.     Rays 


194  NATURAL   PHILOSOPHY. 

of  light  from  A,  after  refraction,  diverge  as  if  they  had 
come  from  a;  rays  from  B,  after  refraction,  diverge  as  if 
they  had  come  from  b;  the  image  will  thus  appear  to  be 
made  at  a  b.  This  image  is  on  the  same  side  of  the  lens, 
smaller  than  the  object,  and  erect. 


SECTION    IV. 
ON    DISPERSION. 

81.  Prisms  refract  light ;  lh?y  also  disperse  it.  They 
separate  white  light  into  rays  of  se^en  different  colors,  —  viz., 

violet,  indigo,  blue, 
green,  yellow,  orange, 
and  red,  —  together  with 
invisible  ra}'s  of  heat  and 
actinism.  (G.  522,  523; 
A.  812,  896.) 

Prisms.  —  Any  trans- 
parent body,  two  of 
whose  sides  are  inclined 
toward  each  other,  is  a 
PRISM.  The  most  com- 
mon form  of  the  prism 
Fig.  109.  js  a  triangular  piece  of 

glass  (Fig.  109).  A  water-prism  may  be  made  by  taking  a 
three-cornered  vessel,  with  glass  sides,  and  filling  it  with 
water.  Other  fluids  may  be  used  in  place  of  water. 

Prisms  refract  Light. — Light,  in  passing  through  prisms, 
must  obey  the  laws  of  refraction.  In  Fig.  110  the  triangle 
m  n  o  represents  a  section  of  a  prism.  A  ra}'  of  light 
striking  its  surface  at  a  will  be  bent  toward  a  perpendicular 
on  entering,  and  from  a  perpendicular  on  emerging,  finally 
taking  the  direction  b  c.  To  the  e}'e  at  c,  this  light  would 
eeem  to  come  from  the  object  at  r  instead  of  L, 


NATURAL  PHILOSOPHY.  195 

Prisms  decompose  Light.  —  The  white  light  that  comes 
from  the  sun,  or  from  other  luminous  bodies,  is  really  made 
tip  of  seven  different  kinds  of  light.  The  way  in  which 


Pig.  110. 

Sir  Isaac  Newton  made  this   great   discovery  is   shown  in 
Fig.  111.     In  the  window- shutter  S,  of  a  darkened  room, 


Fig.  ill. 

he  made  a  small  hole,  and  placed  behind  it  a  prism,  P,  so 
that  the  beam  of  sunlight  could  fall  obliquely  upon  one  of 


196  KATtJfcAL  PHILOSOPHY. 

its  sides.  Without  the  prism  the  beam  of  light  would  have 
gone  straight  forward  to  the  floor,  where  it  would  have  made 
a  round  white  spot ;  but,  being  refracted  by  the  prism,  it  was 
thrown  upon  the  screen  E,  and  an  oblong  image  containing 
seven  different  colors  appeared.  These  colors  were,  in  order 
from  the  top  of  the  image,  violet,  indigo,  blue,  green,  yellow, 
orange,  and  red. 

These  colors  are  separated,  because  the  prism  has  power 
to  bend  some  of  them  more  than  others.  The  violet  ra}'S 
are  bent  most,  the  red  rays  least. 

The  oblong  image  upon  the  screen  is  called  the  SOLAR 
SPECTRUM.  This  separation  of  the  white  light  into  its  con- 
stituent rays  of  different  refrangibility  is  called  DISPERSION. 
The  power  of  a  prism  to  separate  the  color  of  white  light  is 
called  DISPERSIVE  POWER. 


Fig.  112. 

Recomposition.  —  The  prism  in  this  way  enables  us  to 
analyze  white  light,  or  to  find  out  the  colors  of  which  it  is 
made  ;  and  now,  if  by  any  means  we  can  unite  these  seven 
colors,  we  shall  produce  white  light  again.  This  can  be 
done  by  using  any  instrument  ivhich  collects  rays  of  light. 
If  the  ra3*s  fall  upon  a  concave  mirror,  they  will  be  reflected 
to  a  focus,  which  will  be  a  white  spot.  If  the  rays  are 
received  upon  a  double-convex  lens,  they  will  be  refracted 
to  a  focus  (Fig.  112),  and  this  focus  also  will  be  white.  Sir 
Isaac  Newton  collected  the  rays  by  using  a  second  prism, 


NATtTKAL  PHILOSOPHY. 


197 


exactly  like  the  first,  but  placed  beside  it  so  as  to  bend  the 
rays  in  the  opposite  direction  :  the  image  on  the  screen  was 
white. 

82.  A  pure  spectrum  formed  by  sunlight  or  by  starlight  is 
crossed  by  a  great  many  fine  black  lines,  while  the  spectra 
formed  by  light  from  artificial  sources  are  crossed  by  differ- 
ent-colored bright  lines.  (G.  562,  563.) 

A  Pure  Spectrum.  —  In  the  spectrum  obtained  from  a 
beam  of  considerable  width,  as  that  which  comes  through  a 


Fig.  113. 

/ 

round  hole  in  the  shutter,  the  colors  overlap  one  another,  and, 
on  this  account,  are  more  or  less  mixed.  In  order  to  get  the 
colors  pure,  the  opening  must  be  in  the  form  of  a  narrow  slit. 
The  Spectroscope.  —  The  spectroscope  is  an  instrument 
used  in  the  study  of  spectra.  It  is  shown  in  Figs.  113  and 
114. 


198 


NATURAL  PHILOSOPHY. 


The  rays  of  light  from  any  source  enter  the  tube  B  through 
a  narrow  slit  in  the  end,  and  are  made  parallel  by  a  convex 
lens  at  the  other  end.  The}T  then  pass  through  the  prism  P, 
are  decomposed,  and  the  colors  pass  through  the  telescope 
A  to  the  eye  of  the  observer. 

The  black  Lines.  —  The  whole  length  of  the  solar  spec- 
trum, when  seen  by  the  naked  eye,  seems  to  be  colored :  it 
is  a  continuous  spectrum;  but,  when  seen  through  a  spectro- 
scope, a  great  many  fine  black  lines  are  found  to  cross  it,  as 
if  a  delicate  brush,  dipped  in  the  purest  black,  had  been 
drawn  across  it  by  a  skillful  artist.  It  is  a  line  spectrum.  A 


beam  of  sunlight  always  gives  the  same  set  of  lines,  holding 
the  same  relative  position  in  the  spectrum.  A  beam  of  star- 
light gives  a  different  set,  and  the  light  from  different  stars 
gives  each  a  set  of  its  own.  These  lines  are  usually  called 
FRAUNHOFER'S  LINES,  in  honor  of  him  who  first  examined 
them  carefully. 

The  bright  Lines.  —  When  the  light  from  an  artificial 
source  is  passed  through  a  prism,  and  its  spectrum  is  seen 
in  a  spectroscope,  no  black  lines  are  visible,  but  instead  of 
these  there  will  be  seen  lines  of  exceeding  brightness,  and  of 
different  colors.  The  colors  of  these  lines,  and  their  places 


NATURAL  PHILOSOPHY. 


in  the  spectrum,  will  depend  upon  the  substance  whose  flame 
gives  the  light.  If,  for  example,  a  little  common  salt  be 
burned  in  a  hot  gas-flame,  a  yellow  line  of  surprising  bright- 
ness will  always  appear  in  the  yellow  part  of  the  spectrum, 
while  the  metal  potassium  in  the  flame  will  always  give  two 
lines,  one  of  a  brilliant  crimson  color  in  the  red  end  of  the 
spectrum,  the  other  a  beautiful  blue  line  aw  a}'  off  in  the  violet 
end.  Each  substance  gives  a  set  peculiar  to  itself. 

Four  of  these  spectra  are  represented  in  Fig.  115.  No 
attempt  is  made  to  show  the  colors  of  the  lines,  but  their 
relative  positions  are  seen  marked  by  a  scale  along  the  top. 


Pig.  115. 

The  scale  is  pictured  in  the  spectroscope  along  with  the 
spectra,  by  means  of  the  tube  C,  and  marks  the  places  of 
the  lines  with  accuracy.  The  upper  spectrum  in  the  cut  is 
that  of  potassium.  Those  of  rubidium,  thallium,  and  in- 
dium follow. 

The  art  of  detecting  the  presence  of  substances  by  means 
of  the  spectra  obtained  by  igniting  them  is  called  SPECTRUM 
ANALYSIS. 

Invisible  Parts  of  the  Spectrum.  —  A  sensitive  ther- 
mometer, held  in  the  colors  of  the  spectrum,  shows  the 
presence  of  heat ;  and  a  curious  fact  was  first  discovered  by 


200  NATURAL  PHILOSOPHY. 

Herschel,  who  found  that  the  heat  was  more  and  more  intense 
toward  the  red  end,  and,  further,  that  the  thermometer  re- 
vealed the  presence  of  heat  at  some  distance  below  the  red 
where  there  was  no  color  at  all. 

There  is  an  invisible  part  of  the  spectrum,  less  refracted 
than  the  red,  which  shows  itself  as  heat. 

Another  Experiment  was  made  by  Hitter,  who  let  the 
spectrum  fall  upon  a  sheet  of  paper  covered  with  solution  of 
silver-nitrate.  The  pure  white  paper  teas  blackened  b}*  the 
spectrum.  And,  what  was  more  surprising,  Hitter  found  that 
this  effect  was  produced  upon  the  paper  to  quite  a  little 
distance  beyond  the  violet  where  there  was  no  color. 

There  is  an  invisible  part  of  the  spectrum,  more  refracted 
than  the  violet,  which  shows  itself  by  chemical  action. 

The  Energy  of  the  Sunbeam.  —  Heat,  colors,  and 
chemical  action  are  the  three  manifestations  of  the  energy  in 
the  sunbeam.  The  sunbeams  themselves  are  only  undula- 
tions from  the  sun.  But  these  undulations  are  compound. 
They  are  made  up  of  a  multitude  of  simple  waves  differing 
greatly  in  their  lengths  and  periods.  These  compound 
waves  break  against  the  face  of  nature,  and  the  molecules 
of  bodies  are  put  in  motion  by  them. 

The  energy  of  this  molecular  vibration  at  certain  rates  is 
heat,  at  certain  more  rapid  rates  is  color,  and  at  still  more 
rapid  rates  is  actinism.  / 

83.  Heat  tends  to  diffuse  itself  equally  among  all  bodies. 

The  amount  of  heat  which  a  body  can  radiate  depends 
upon  its  temperature,  its  nature,  and  the  condition  of  its 
surface. 

The  equal  Diffusion  of  Heat.  —  If  two  bodies,  one  cold, 
the  other  hot,  be  placed  near  each  other,  it  will  in  a  short 
time  be  found  that  both  are  equally  warm.  The  cold  body 
has  received  more  heat,  the  hot  bod}-  has  parted  with  some 
that  it  had.  What  is  thus  true  of  two  bodies  is  true  of  all. 
Bodies  are  constantly  giving  and  receiving  heat.  Those 


NATURAL  PHILOSOPHY.  201 

which  part  with  more  than  they  receive  from  others  grow 
colder ;  those  which  receive  more  than  they  give  grow 
warmer.  Ice,  for  example,  is  giving  heat  to  all  bodies 
around  it ;  it  is  at  the  same  time  receiving  heat  from  them 
in  return.  Ice  will  actually  warm  a  body  which  is  colder 
than  itself,  because  it  will  give  more  heat  than  it  gets  in  re- 
turn ;  it  will  be  melted  by  a  body  warmer  than  itself,  because 
it  receives  more  than  it  gives. 

Transmission  of  Heat-Rays.  —  Just  as  light  passes 
more  freely  through  some  bodies  than  through  others,  so  the 
dark  rays  of  radiant  heat  pass  through  different  bodies  with 
different  degrees  of  facility.  Those  bodies  through  which 
heat  passes  most  freely  are  said  to  be  diathermic,  while  those 
through  which  it  can  go  with  the  greatest  difficulty  are  said 
to  be  athermic. 

Heat  from  different  sources  is  transmitted  in  different 
degrees  through  the  same  substance.  It  is,  for  example,  a 
familiar  fact,  that  the  glass  of  our  windows  allows  the  heat 
of  the  sun  to  enter  our  rooms,  while  it  prevents  the  heat  of 
the  stove  from  going  out. 

Rock-salt  is  the  most  diathermic  substance  known ;  it 
allows  heat  from  all  sources  to  pass  through  .t  with  the 
greatest  freedom. 

Depends  on  Temperature,  Nature,  Condition.  —  The 
higher  the  temperature  of  a  body,  the  more  heat  it  can  radi- 
ate. Moreover,  bodies  of  different  substance,  when  at  the 
same  temperature,  give  off  different  quantities  of  heat  in  the 
same  time.  Thus  iron  is  a  better  radiator  than  gold.  Still 
further,  the  same  bod}',  at  the  same  temperature,  with  a 
rough  surface  will  radiate  much  faster  than  when  its  surface 
is  smooth.  The  rough  surface  of  a  cast-iron  stove,  for  ex- 
ample, is  a  better  radiator  than  if  it  were  polished. 

84.  Drops  of  rain  may  decompose  the  sunlight:  in  this 
way  the  rainbow  is  produced.  The  primary  bow  consists  of 
bands  of  the  seven  colors  of  the  spectrum,  arranged  in 
parallel  arches,  with  the  red  band  on  the  outside. 


202 


NATTJBAL  PHILOSOPHY. 


In  the  secondary  bow  the  order  of  the  colored  arches  is 
changed,  the  violet  being  on  the  outside. 

The  Primary  Rainbow.  —  This  most  beautiful  phenome- 
non is  produced  by  the  action  of  rain-drops  ;  they  decom- 
pose the  sunlight,  and  send  its  rich  colors  to  the  eye. 

To  understand  this  action,  suppose  the  circle,  whose  center 
is  at  C  (Fig.  116),  to  represent  a  section  of  a  drop  of  water. 

Rays  of  sunlight  (S  A) 
falling  upon  the  upper 
part  of  the  drop  will  be 
refracted  to  the  point  B. 
At  this  point  a  part  of 
the  light  will  pass  out  in- 
to the  air  again,  but  an- 
other part  will  be  reflect- 
ed by  the  inner  surface 
of  the  water,  and  strike 
Fig'116'  the  surface  at  another 

point,  D.  The  light  which  here  goes  out  of  the  drop  into 
the  air  will  be  again  refracted.  The  light  will  not  only  be 
refracted,  in  its  passage  through  the  drop :  it  will  be,  at  the 
same  time,  decomposed.  On  coming  out  of  the  water  the  red 
rajr,  bent  least,  will  take  a  direction  represented  by  D  E ; 
the  violet  ray,  bent  most,  may  be  represented  by  D  V ;  and 
all  the  other  colors  of  the  spectrum  will  be  found  between 
these. 

The  red  Band  is  on  the  Outside.  —  Now,  it  is  quite 
clear  that  if  the  person  were  standing  upon  the  ground  in 
the  direction  of  D  E,  so  that  the  red  rays  from  this  drop 
would  enter  his  ej-e,  the  violet  rays,  and  indeed  all  the  other 
colors,  would  go  over  his  head.  To  him  this  drop  of  water 
would  appear  red.  Another  drop,  some  distance  below  this 
one,  would  send  violet  rays  into  the  same  eye.  Between  the 
drop  which  sends  the  red,  and  that  which  sends  the  violet, 
there  would  be  others  from  which  the  eye  would  receive  the 
other  colors  of  the  spectrum.  (Fig.  117.) 


NATURAL   PHILOSOPHY.  203 

Hence,  when  a  shower  of  rain  is  falling,  and  the  sun  is  at 
the  same  time  shining  in  the  opposite  part  of  the  sky,  so 
that  a  person  looking  toward  the  shower  will  have  his  back 

turned  toward  the  sun,  he 
will  see  the  seven  colors  of 
the  spectrum  painted  upon 
the  cloud  in  order,  with  red 
at  the  top  and  violet  at  the 
bottom. 

The  Colors  are  in  the 
Form  of  an  Arch. — Now, 

suppose  a  line  drawn  from 
Fig.  117.  j^g  gun  though  tne  eve  of 

the  observer,  and  straight  onward  until  it  reaches  a  point  O 
(Fig.  116),  directly  under  the  drop  C,  which  sends  the 
light  to  the  eye.  If  this  drop  sends  a  red  ray  to  the  eye, 
then  all  others,  which  like  this  are  opposite  the  sun,  and 
whose  distances  from  O  are  the  same,  will  also  give  red  rays. 
If  the  arc  of  a  circumference  be  drawn  with  O  as  a  center, 
and  with  a  radius  C  O,  all  drops  along  this  circumference 
will  be  equally  distant  from  the  center  O,  and  will  therefore 
give  red  rays.  The  red  part  of  the  rainbow  is,  for  this 
reason,  a  circular  arch,  and,  for  the  same  reason,  the  other 
colors  are  parallel  arches  below  the  red. 

The  Secondary  Bow.  —  Outside  of  the  bow  just  ex- 
plained, another,  the  secondary  bow,  is  often  seen.  Its 
colors  are  more  dim,  and  their 
order  is  reversed,  the  violet 
being  at  the  top  and  the  red 
at  the  bottom. 

To  explain  the  primary  bow 
we  trace  rays  of  light  falling 
upon  the  top  of  the  drops  of 
water.  But  drops  of  rain  in 

the  air  are  entirely  covered  with  light,  and,  to  explain  the 
secondary  bow,  we  may  trace  the  rays  which  fall  upon  their 


204  NATURAL   PHILOSOPHY. 

lower  parts.  The  diagram  (Fig.  118)  illustrates  this.  A 
beam  of  light,  S  A,  is  refracted  at  A,  reflected  at  B,  and 
again  at  D,  and  refracted  at  F,  finally  entering  the  eye  in 
the  direction  of  G.  If  F  G  represents  the  red  ray,  then 
F  V  may  represent  the  violet  ray  which  is  more  refracted. 
Hence  the  drop  which  sends  the  violet  ray  to  the  eye  must 
be  above  that  which  sends  the  red  ;  and  the  violet  band  is 
on  the  outside. 

85.  Bodies  are  of  different  colors,  only  because  they  de- 
compose the  sunlight,  and  reflect  different  parts  of  it  to  the 
eye.  The  various  colors  of  the  sky  and  the  clouds  are 
due  to  the  decomposition  of  the  light  wrhich  comes  through 
them  from  the  sun.  (G.  555  ;  A.  913.) 

The  Color  of  Bodies.  —  The  sun  sheds  a  flood  of  pure 
white  light  upon  all  bodies  alike.  This  white  light  is  decom- 
posed at  their  surfaces.  Some  of  its  colors  are  transmitted 
or  absorbed  by  the  body,  while  the  others  are  reflected  to 
the  eye.  One  bod}7  is  red  because  it  decomposes  the  sun- 
light, and  reflects  the  red  rays ;  another  is  blue,  because  it 
reflects  only  blue  rays.  The  foliage  of  trees  in  the  spring- 
time receives  the  sun's  white  light,  decomposes  it,  and  re- 
flects only  the  green  rays.  The  petals  of  the  violet  decom- 
pose the  sunlight  to  share  with  us  the  beautiful  colors  of 
the  spectrum ;  it  reflects  the  colors  of  the  violet  end,  and 
keeps  to  itself  those  of  the  other.  A  body  which  reflects  all 
the  color  of  the  light  it  receives  is  white  ;  one  which  reflects 
none  is  black. 

That  which  is  absorbed  becomes  heat  or  chemical  action. 

The  Color  of  the  Sky.  —  The  sky,  when  free  from  clouds, 
is  blue,  because  the  particles  of  the  atmosphere  reflect  blue 
rays  of  light.  If  the  thin  air  could  not  reflect  light  at  all, 
the  sky  would  appear  black :  if  it  reflected  it  without  de- 
composition, it  would  be  white.  The  white  sunlight  falls 
upon  its  molecules,  is  decomposed  by  them,  and  only  those 
rays  which  make  up  the  delicate  blue  color  of  the  sky  are 
reflected  to  our  eyes. 


NATURAL   PHILOSOPHY.  205 

The  Color  of  the  Clouds.  —  The  clouds  both  reflect  and 
refract  the  sunlight,  and  all  their  varied  colors  are  due  to  the 
decomposition  thus  produced.  There  can  be  no  more  gor- 
geous display  of  colors  than  we  often  see  upon  the  clouds  of 
the  morning  and  the  evening  sky.  What  grand  and  diversi- 
fied effects  to  be  produced  by  means  of  such  simple  materials 
as  light,  water,  and  air  ! 

86.  The  colors  of  the  spectrum  may  be  also  produced  by 
the  interference  of  light-waves. 

This  furnishes  a  means  of  measuring  the  wave-lengths, 
which  are  found  to  vary  from  .0000266  of  an  inch  for  red  to 
.0000167  for  violet. 

"  Diffraction  fringes  "  are  the  effect  of  interference.  (G. 
627,  630,  631.) 

Sound  and  Light  alike.  —  We  have  learned  that  light 
is  the  result  of  vibrations  in  a  very  elastic  medium  called 
ether.  We  ought,  therefore,  to  expect  that  the  phenomena 
of  light  would,  in  many  respects,  be  like  those  of  sound  and 
heat.  We  have  found  this  to  be  true,  their  laws  of  reflec- 
tion, refraction,  and  transmission  being  alike.  They  are 
alike  also  in  regard  to  interference.  ^ 

Interference  of  Sound.  —  If  two  sound-waves  in  air 
cross  each  other,  so  as  to  bring  their  condensed  parts  or 
phases  together,  they  cause  a  wave  whose  amplitude  is  equal 
to  the  sum  of  theirs,  and  produce  a  sound  of  greater  inten- 
sity. If  they  come  together  in  such  wa}T  that  the  condensed 
phase  of  one  strikes  the  rarefied  phase  of  the  other,  they 
cause  a  wave  whose  amplitude  is  equal  to  the  difference  of 
theirs,  and  produce  a  sound  of  less  intensity. 

Thus  two  sounds  may  together  produce  silence. 

Interference  of  Light. —  So,  too,  if  waves  of  light,  in 
the  ether,  cross  each  other  so  as  to  bring  their  like  phases 
together,  they  cause  a  wave  whose  amplitude  is  equal  to  the 
sum  of  theirs,  and  produce  a  light  of  greater  brightness ; 
but,  if  their  opposite  phases  are  thrown  together,  they  form 


206  NATURAL   PHILOSOPHY. 

a  single  wave  whose  amplitude  is  equal  to  their  difference  , 
and  cause  a  light  of  less  intensity. 

Thus  two  rays  of  light  may  together  produce  darkness. 

The  Conditions.  —  Now,  examine  the  conditions  of  in- 
terference more  carefully.  A  wave  consists  of  two  phases, 
and  the  sum  of  their  lengths  is  the  length  of  the  wave.  Of 
course,  then,  each  phase  is  just  one  whole  wave-length 
ahead  of  the  next  one  behind  it  of  the  same  name,  and  just 
one-half  a  wave-length  ahead  of  the  next  one  behind  it  of 
a  different  name.  If,  then,  two  sets  of  waves  are  to  inter- 
fere with  like  phases  together,  their  starting-points  must  be 
one  wave-length,  or  some  whole  number  of  wave-lengths^ 
apart.  To  bring  different  phases  together,  the  distance  be- 
tween their  starting-points  must  be  one-half  a  wave-length,  or 
some  odd  number  of  half  wave-lengths  apart. 

If  the  two  sets  have  equal  amplitude,  their  interference  in 
like  phases  will  give  a  double  brightness,  but  in  unlike  phases 
will  result  in  darkness. 

The  Length  of  Light-  Waves.  —  Light  of  all  colors 
travels  with  the  same  velocity  ;  and,  since  violet  is  produced 
by  the  most  rapid  vibrations,  the  length  of  its  waves  must 
be  less  than  for  any  other.1  Suppose,  now,  that  two  sets  of 
waves  start  from  surfaces  very  near  to  each  other,  but  not 
parallel  :  at  some  points  the  distance  between  the  starting- 
points  of  two  waves  will  correspond  to  the  wave-length  for 
violet  ;  at  others,  to  the  wave-lengths  of  other  colors.  The 
result  of  the  interference  of  the  two  sets  of  waves  will  be  to 
form,  at  different  points,  all  the  tints  of  the  spectrum.  The 
rainbow  colors  of  the  soap-bubble,  which  so  delighted  us  in 
childhood,  illustrate  this  most  beautifully.  The  light  is  re- 
flected from  both  the  outside  and  the  inside  surfaces  of  the 
thin  film  ;  these  surfaces  are  not  parallel  ;  and  the  interfer- 
ence of  the  two  sets  of  waves  gives  rise  to  the  colors. 

The  Measurement.  —  Now,  could  we   but   measure  the 


1  Wave-length  =  ;  or,  L  =  „.     This  is  true  for  waves  of  every  name,  in 

water,  air,  or  ether. 


NATURAL   PHILOSOPHY. 


207 


thickness  of  the  film   at  the   point  where   red  is   seen,  we 

could  find  the  length  of  the  wave  for  red ;  and,  if  at  points 

where  other  colors  appear,  we  could  find  the  wave-lengths 

which   produce    them.      Newton    actually   calculated   these 

minute   spaces,  although,  of  course,  so   frail   a  thing  as  a 

soap-bubble  could  not   be  used  for  the  purpose.     His  plan 

may  be  understood  from  Fig.  119.     A  very  thin  layer  of  air 

is  included  between  two  very   smooth  glass   surfaces,  one 

curved,    the    other    plane. 

When    the    glasses   are 

pressed   together,    a   series 

of   rainbow- colored    rings, 

Newton's  rings,   are    seen, 

with   a  black  center  at  the 

point  a,  where  the  glasses 

are  in  contact.     If  red  light 

alone  is  used,   a  series  of 

red  rings  will  be  separated 

by  dark  spaces. 

Now,  these  rings  are 
caused  by  the  interference 
of  two  sets  of  waves,  one 
reflected  from  the  lower 
side  of  the  curved  glass,  the  other  from  the  upper  side  of  the 
plane  glass,  meeting  at  the  63-6,  E.  Newton  calculated  the 
thickness  of  the  layer  of  air  at  points,  bcde,  where  the  rings 
were  seen,  and  from  these  thicknesses  calculated  the  length 
of  the  waves.  The  more  refrangible  colors  are  produced 
by  shorter  waves.  The  lengths  of  luminous  waves  vary  be- 
tween .0000167  of  an  inch  for  violet,  and  .0000266  of  an 
inch  for  red. 

Color  depends  upon  Rapidity  of  Vibration.  —  As  the 
pitch  of  sounds  depends  upon  the  rapidity  of  the  undula- 
tions of  air,  so  the  color  of  light  varies  with  the  rapidity  of 
undulations  of  ether.  A  red  light  is  made  by  the  slowest,  a 
violet  light  by  the  swiftest,  vibrations. 


e  d 


208 


NATURAL   PHILOSOPHY. 


The  e}*e  is  affected  by  undulations  between  the  limits  of 
about  392  millions  of  millions  a  second  for  red,  to  about  754 
millions  of  millions  for  violet.1 

Diffraction.  —  Diffraction  is  the  change  which  light  un- 
dergoes when  it  passes  the  edge  of  an  opaque  obstacle. 

Experiment.  —  A  beam  of  sunlight  L  (Fig.  120),  com- 
ing through  a  narrow  slit  in  the  shutter  of  a  darkened  room, 

S 


Fig.  120. 

is  made  to  pass  through  a  second  slit  O,  at  a  distance  of  ten 
or  fifteen  feet.  When  a  white  screen,  S  (a  front  view  shown 
at  S),  is  placed  behind  this  slit,  a  distance  of  about  four 
feet,  a  multitude  of  colored  bands,  alternating  with  dark 
spaces,  will  appear  upon  it. 

Explanation.  —  Diffraction  fringes  are  caused  by  the  in- 
terference of  light.  When  one  set  of  waves  passes  the  edge 
of  an  obstacle,  it  starts  another  set  in  the  ether  be}'ond. 
Two  new  sets  of  waves  are  in  this  way  started  from  the  op- 
posite edges  of  the  slit  in  the  shutter.  These  two  sets  going 
almost,  but  not  exactly,  in  the  same  direction,  interfere  and 
give  rise  to  the  many  colored  bands. 

Illustrations  of  Diffraction. — Place  two  knife-blades 
edge  to  edge,  and  look  through  the  narrow  slit  between  them 
at  the  clear,  bright  sky.  Instead  of  a  well-defined,  clear, 
bright  space,  a  great  number  of  very  delicate  parallel  black 
lines  will  be  seen.  The  edge  of  a  single  blade,  or  of  any 
thin  body,  will  appear  fringed  with  dark  lines,  and,  under 
some  circumstances,  with  colored  bands  of  great  beauty. 

velocity  of  light         186,000  miles 
1  **"  lor  Vl°let  -      wavelength-  =  .000167  inch  ' 


NATURAL  PHILOSOPHY.  209 

One  who  has  been  taught  to  recognize  it,  will  be  surprised 
to  find  how  numerous  and  common  are  the  various  forms  of 
this  delicate  phenomenon.  A  lady,  on  suddenly  lifting  her 
eyes  to  the  bright  sky,  often  sees  it,  through  the  meshes  of 
her  veil,  covered  with  a  net-work  of  rairbows.  Who  has 
not  wondered  at  the  brilliant  colors  of  the  sky,  seen  through 
the  fine  fibres  of  a  bird's  feather? 


SECTION  V. 

ON  OPTICAL  INSTRUMENTS. 

87.  The  microscope,  the  telescope,  and  many  other  instru- 
ments, help  the  eye  to  see  small  or  distant  objects,  by  form- 
ing large  and  perfect  images  of  them  near  by,  for  it  to 
examine. 

The  eye  itself  is  an  optical  instrument  of  the  most  perfect 
construction.  (G.  565,  566,  567,  571,  576.) 

The  Simple  Microscope.  —  The  simple  microscope  con- 
sists of  a  single  convex  lens.  The  lens  is  held  in  the  hand 
at  a  little  less  than  its  focal  distance  from  the  object.  The 


Fig.  121. 

eye  receives  the  light  which  comes  from  the  object  through 
the  glass,  and  sees  a  magnified  image  on  the  other  side.  In 
Fig.  121  the  object  is  a  small  insect,  a  b. 

The   Compound   Microscope.  —  The   operation   of  the 
compound  microscope  may  be   understood  by  means   of  a 


210  NATURAL  PHILOSOPHY. 

diagram  (Fig.  122).  It  consists  of  at  least  two  convex 
lenses. 

The  lens  A,  called  the  object-glass,  refracts  the  light  from 
the  object  O,  placed  a  little  be3'ond  its  focus,  and  forms  an 
image  inverted  at  O'.  The  light  from  this  image  is  refracted 
by  another  lens  B,  called  the  eye-glass;  and,  if  the  rays  are 
received  into  the  eye,  they  will  appear  to  have  come  from 
C  D,  which  is  the  magnified  image  of  the  object. 

In  a  good  microscope  these  glasses  are  not  single  convex 
lenses :  each  is  a  combination  of  two  or  more.  A  single 
convex  lens  can  not  give  an  image  sharply  defined  and  free 
from  unnatural  colors,  but  combinations  can  be  made  to  do 
this. 


Pig.  122. 


B}^  means  of  this  instrument,  things  otherwise  too  small 
to  be  seen  are  made  visible,  and  a  world  of  wonderful 
creations  is  thus  revealed  for  the  study  and  admiration  of 
man.  A  drop  of  water  from  a  stagnant  pool  is  found,  by 
means  of  the  microscope,  to  be  swarming  with  living  crea- 
tures, whose  forms  are  perfect  and  whose  appetites  are  not 
unlike  those  of  larger  animals. 

The  Telescope.  —  A  telescope  is  used  for  viewing  distant 
objects.  Sometimes  a  lens  is  employed  to  form  an  image  ; 
sometimes  the  image  is  formed  by  a  mirror.  In  the  first 
case,  the  instrument  is  called  a  REFRACTING  TELESCOPE  ;  in 
the  second,  it  is  called  a  REFLECTING  TELESCOPE. 

Of  the  refracting  telescope  there  are  three  important  forms  : 
Galileo's,  the  astronomical,  and  the  terrestrial. 


NATURAL  PHILOSOPHY. 


211 


In  Galileo's  Telescope  there  is  a  double  convex  object- 
glass  M  N  (Fig.  123),  and  a  double  concave  eye-glass,  E  F. 


Fig.  123. 

Rays  of  light  from  the  point  A  of  a  distant  object  A  B,  after 
passing  through  the  two  glasses,  diverge  as  if  they  came  from 
the  point  a',  while  ra}Ts  from  the  point  B  of  the  object  after  re- 
fraction diverge  as  if  from  the  point  &'.  An  erect  image,  a  6, 
will  be  seen  by  holding  the  eye  in  front  of  the  eye-glass  E  F. 

The  opera-glass  consists  of  two  small  Galilean  telescopes 
placed  side  by  side. 

In  the  Astronomical  Telescope,  two  double  convex 
lenses  are  used.  The  object-glass  O  (Fig.  124)  forms  a 
small  image  a  6  of  a  distant  object  A  B.  The  eye-glass, 


Pig.  124. 

E,  being  so  placed  that  its  focus,  F,  is  a  little  beyond  this 
image,  refracts  the  light,  so  that  it  will  appear  to  have  come 
from  a  magnified  image  c  d.  The  course  of  the  rays  may 
be  traced  in  the  figure.  In  this  instrument  the  image  is 
always  inverted. 


212  NATURAL  PHILOSOPHY. 

The  Terrestrial  Telescope  is  used  for  viewing  distant 
objects  upon  the  earth.  To  see  them  upside  down,  as  in  the 
astronomical  telescope,  is  not  desirable :  that  they  may  be 
seen  right  side  up,  two  convex  lenses  are  placed  between 
the  object-glass  and  the  e3*e-glass.  The  arrangement  of  the 
glasses,  and  the  course  of  the  rays,  are  shown  in  Fig.  125. 
The  object-glass  O  forms  a  small  inverted  image,  I,  of  a  dis- 


Fig.  125. 

tant  object,  A  B,  near  its  focus.  From  this  image  the  light 
goes  through  the  two  lenses,  ra  and  n,  to  form  a  second 
image  L.  This  image  is  erect  with  respect  to  the  object, 
and  it  is  magnified  by  the  e}Te-glass  E,  in  the  usual  manner. 

Reflectors.  —  Of  the  reflecting  telescope  there  are  several 
varieties.     In  all  of  them  the  image  of  a  distant  object  is 


Fig.  126. 

formed  by  a  concave  mirror,  and  this  image  is  magnified  by 
a  convex  eye-glass. 

In  the  Herschelian  Telescope    (Fig.    126),  the   mirror 
M  N  is  inclined  to  the  axis  of  the  tube  in  which  it  is  placed, 


KATTTHAL  PHILOSOPHY. 


213 


so  that  rays  of  light  from  a  distant  object  will  be  reflected 
to  a  focus  near  to  one  side  of  the  tube  at  the  other  end. 
The  observer,  looking  down  into  the  tube,  holds  an  eye- 
piece, A,  in  his  hand,  through  which  he  views  a  magnified 
image. 

The  Magic-Lantern.  —  The  magic-lantern  is  an  instru- 
ment by  which  the  image  of  a  small  object,  greatly  mag- 
nified, may  be  thrown  upon  a  screen. 

It  consists  of  a  convex  lens,  with  objects  highly  illumi- 
nated by  lamp-light  placed  so  near  it,  that  their  images  are 
formed  far  away.  Fig.  127  shows  a  section  of  the  instru- 


Fig.  127. 

ment.  Inside  of  a  dark  box,  a  strong  light,  L,  is  placed. 
Behind  this  light  is  a  concave  mirror,  M,  and  in  front  of  it 
a  convex  lens  A.  This  lens  is  at  the  entrance  of  a  tube 
which  projects  from  the  side  of  the  box.  Inside  this  tube 
slides  a  smaller  one,  in  which  is  fixed  another  powerful  lens. 
The  picture  is  placed  in  a  slit,  C,  provided  for  it  in  the  larger 
tube,  just  in  front  of  the  first  lens.  The  lamp  fills  the  box 
with  a  strong  light.  The  lens  A,  receiving  light  directly 
from  the  lamp,  and  reflected  from  the  mirror,  condenses  it 
upon  the  object,  and  highly  illuminates  it.  The  light  from 
this  bright  object  goes  on  through  the  second  lens  to  the 
distant  screen,  and  there  forms  a  large  and  perfect  image. 

The  stereopticon,  so  largely  used  by  lecturers  and  teach- 
ers, is  a  magic-lantern  with  lenses  of  superior  quality,  and 
in  which  the  lime-light  or  the  electric  light  is  used. 


214  NATURAL  PHILOSOPHY. 

The  Camera-Obscura.  —  The  camera-obscura  is  an  in- 
strument by  which  to  form  miniature  images  of  objects.  It 
consists  of  a  dark  box,  a  section  of  which  is  represented  by 
A  B  (Fig.  128),  containing  a  screen,  S,  and  having  a  double 
convex  lens,  L,  filling  an  opening  in  one  end.  The  distance 
of  the  lens  from  the  screen  may  be  varied  b}*  sliding  the 
tube  which  carries  it  back  and  forth  in  the  larger  tube  C. 
The  light  from  the  object  O  is  refracted  by  the  lens,  and  a 
beautiful  image  is  formed  upon  the  screen.  This  image  is 
always  inverted,  and  smaller  than  the  object. 

The  camera  may  be  illustrated  b}r  a  ver}'  simple  experi- 
ment. If,  in  a  hole  in  the  shutter  of  a  darkened  room,  is 
placed  a  double  convex  lens,  the  room  is  itself  a  camera- 
obscura.  Let  a  white  screen  be  placed  in  front  of  the  lens 


Fig.  128. 

at  a  proper  distance,  and  it  is  at  once  covered  with  a  perfect 
picture  of  whatever  scenery  may  be  outside.  Houses  and 
distant  hills,  the  sky  with  its  floating  clouds,  men  and 
animals  in  the  street,  and  'even  the  flying  birds,  and  the 
curling  smoke,  are  distinctly  painted  in  miniature  upon  the 
screen. 

The  Eye.  —  But  most  perfect  of  all  optical  instruments 
is  the  eye.  Who  could  at  first  believe,  that  in  describing, 
as  we  have  done,  the  camera-obscura,  we  were  describing 
a  rough  model  of  the  human  e}Te  !  Yet  the  eye  is  a  camera- 
obscura,  differing  from  the  common  form  of  that  instrument 
only  in  its  wonderful  perfection. 

The  human  eye  is  a  gobular  chamber,  having  for  its  outer 
wall  a  hard  tough  membrane  called  the  SCLEROTIC  COAT. 
The  front  part  of  the  sclerotic  coat  is  a  transparent  sub- 


PHILOSOPHY. 


S16 


stance  called  the  CORNEA.  The  chamber  is  lined  with  a  more 
delicate  membrane  called  the  CHOROID,  and,  to  insure  the 
darkness  of  the  place,  this  is  covered  upon  the  inside  with  a 
black  paint.  The  front  part  of  the  choroid  coat  is  called  the 
IRIS,  and  in  the  center  of  this  is  a  round  hole  called  the 
PUPIL  of  the  eye,  through  which  light  may  pass  into  the  dark 
chamber  bej'ond.  Behind  this  opening  is  a  double  convex 
lens,  very  transparent  and  considerably  hard,  called  the 
CRYSTALLINE  LENS.  Between  this  lens  and  the  cornea  is  a 
limpid  liquid  called  the  AQUEOUS  HUMOR  ;  and  filling  the  dark 
chamber,  behind  the  lens,  is  another  fluid,  called  the  VITRE- 


Fig.  129 

ous  HUMOR.  The  arrangement  of  these  parts  may  be  under- 
stood by  attentively  studj'ing  Fig.  129,  which  represents  a 
section  of  the  eye.  S  S  is  the  outer  or  sclerotic  coat,  some- 
times called  the  white  of  the  e}re.  c  c  is  the  cornea ;  it  is 
more  convex  than  the  sclerotic.  K  K  is  the  choroid,  and 
i  i  is  the  iris,  the  vertical  curtain  which  shuts  out  all  light, 
except  what  may  get  through  the  hole  at  its  center,  —  the 
pupil.  L  L  is  the  ciystalline  lens,  and  the  large  chamber 
V  is  filled  with  the  vitreous  humor.  The  course  of  the  rays 
of  light  is  also  shown  in  the  figure.  An  inverted  image  of 
an  object,  O,  is  formed  at  R.  It  is  there  received  upon  a 
net-work  of  delicate  nerve-fibers  called  the  RETINA,  R  R. 


216  NATURAL  PHILOSOPHY. 

The  mind  takes  cognizance  of  this  picture,  and  the  person 
is  said  to  see  the  object  O.  These  pictures  on  the  retina  are 
always  smaller  than  the  objects,  and,  the  more  distant  the 
object,  the  more  minute  the  image.  The  diameter  of  the 
eye  is  little  more  than  an  inch ;  and  yet  when  a  person  sees 
an  extended  landscape,  every  visible  object,  far  and  near,  is 
painted  upon  the  inner  lining.  If  the  picture  in  the  human 
eye  be  thus  minute,  what  must  it  be  in  the  eye  of  a  canary- 
bird  or  butterfly ! 

SECTION  VI. 

ON  DOUBLE  REFRACTION  AND  POLARIZATION. 

88.  When  a  beam  of  light  passes  through  a  crystal  of 
Iceland  spar,  it  is  doubl}r  refracted.  The  two  beams  which 
emerge  are  both  polarized.  Light  may  be  also  polarized  by 
reflection.  The  effects  of  polarized  light  are  numerous 
and  important.  (G.  636,  642,  645,  646,  655,  658,  661.) 

Double  Refraction.  —  A  crystal  of  Iceland  spar  is 
ver}r  transparent,  and  its  form  (Fig.  130)  is  as  regular  as 
could  be  cut  by  the  hand  of  a  skillful  artist.  Each  of  its 


Fig.  130. 

six  surfaces  is  a  parallelogram.  They  are  so  arranged  that 
three  of  them  have  each  an  obtuse  angle  at  A,  and  the  other 
three  each  an  obtuse  angle  at  the  opposite  corner,  at  A' 


NATORAL  £ HILOSOPH*. 


217 


in  the  crystal  B  in  the  figure.  A  line  joining  the  points 
A  and  A'  is  called  the  OPTIC  Axis  of  the  crystal.  If  the 
edges  of  the  crystal  are  all  equal  the  axis  is  a  diagonal,  but 
if  not  then  the  axis  is  not  a  diagonal  of  the  costal.  Both 
cases  are  shown  in  the  cut.  Now,  if  a  ray  of  light  be  passed 
through  such  a  crystal  in  any  direction  not  parallel  to  the 
axis,  it  will  emerge  as  two  separate  rays,  and  the  light  will 
be  said  to  be  doubly  refracted. 

Double  refraction  causes  the  curious  effect  of  making  any 
thing  on  which  the  crystal  rests  appear  to  be  double.  (Fig. 
131.)  One  of  these  refracted  beams  obeys  the  regular  law 
of  refraction ;  the  other  does  not.  The  first  is  called  the 


Pig.  131. 

ORDINARY  beam,. the  other  the  EXTRAORDINARY  beam.  Many 
other  transparent  crystals  have  this  power  of  double  refrac- 
tion. 

Both  Beams  are  polarized.  —  A  very  curious  change 
is  wrought  in  the  light  by  double  refraction.  Common  light 
will  pass  through  any  transparent  medium,  no  matter  in  what 
position  it  may  be  held  ;  but  these  doubly  refracted  rays  are 
able  to  pass  through  a  second  medium  when  it  is  held  in 
certain  positions  only.  For  example,  if  the  ordinary  beam 
be  made  to  fall  upon  a  flat  plate  of  tourmaline  (a  transparent 
mineral  crystal),  and  it  go  through  when  in  one  position,  it 
will  not  go  through  when  the  plate  has  been  turned  90° 


218  NATURAL  PHILOSOPHY* 

around.  Turn  the  plate  90°  more,  and  the  beam  will  agaiti 
pass  through  it ;  turn  it  90°  farther  yet,  and  the  beam  will 
be  again  wholly  cut  off* 

If  the  extraordinary  beam  be  tried,  it  Will  be  wholly  trans- 
mitted by  the  plate  in  positions  where  the  ordinary  beam 
was  cut  off,  and  wholly  cut  off  where  the  other  was  trans- 
mitted. 

When  light,  by  being  refracted  or  reflected,  is  made  inca- 
pable of  being  again  refracted  or  reflected  except  in  certain 
directions,  it  is  said  to  be  polarized. 

Polarization  by  Reflection.  —  If  a  beam  of  light,  shown 
by  a  b  (Fig.  132) ,  falls  upon  a  plate  of  black  glass  at  an 

angle    of    incidence 
54^-°,    a   part    of    it 
will    pass    into   the 
,  glass,  the  rest  of  it 
will  be  reflected.     If 
the  reflected  part  be 
examined  by  a  plate 
Fig>  132'  of  tourmaline,  it  will 

be  found  to  be  polarized.  Or  if  another  plate  of  black  glass, 
N,  is  placed  parallel  to  the  first,  the  beam  will  be  reflected  as 
the  figure  shows  it ;  brt  let  the  plate  be  turned  90°,  as  shown 
by  the  dotted  lines,  and  the  beam  will  be  wholly  cut  off. 
Turn  it  90°  farther,  and  the  reflected  beam  appears  again ; 
another  90°,  and  it  is  again  cut  off.  At  an}*-  other  angle  of 
incidence  than  54^°,  the  light  will  be  only  partly  polarized : 
54l°  is  the  polarizing  angle  for  glass. 

Polarizing  Instruments.  —  The  instruments,  called  po- 
lariscopes,  by  which  to  study  polarized  light,  consist  essen- 
tially of  two  parts,  one  to  polarize  the  light,  the  other  to 
examine  it  after  it  has  been  polarized.  The  first  is  called 
the  POLARIZER,  the  second  the  ANALYZER.  One  of  the 
simplest  forms  of  the  instrument  is  shown  in  the  figure  (Fig. 
133).  The  polarizer,  P,  is  a  plate  of  glass,  covered  on  the 
back  of  it  with  black  varnish.  The  analyzer,  A,  is  a  plate 


NATUKAL  PHILOSOPHY. 


219 


of  tourmaline  set  into  a  movable  tube.  Objects  to  be 
examined  by  polarized  light  are  supported  in  a  movable 
ring  O. 

Theory   of    Polarization.  —  To    explain    the    phenom- 
na  of  polarization,  we  must  remember  that  light  consists 


Fig.  133. 

of  undulations,  and  add  to  this  the  assumption  that  the 
vibrations  of  the  ether-particles  take  place  in  all  possible 
directions  at  right  angles  to  the  direction  in  which  the  ray  it- 
self is  going.  Let  us  for  a  moment  suppose  that  we  could 
see  the  ether,  and  that  we  look  squarely  at  the  end  of  a 
beam  of  light.  We  may  fancy  that  we  should  see  a  circular 
outline,  with  the  particles  of  ether  moving  swiftly  in  the 
directions  of  all  its  diameters.  Let  A  (Fig.  134)  represent 
this  view.  Now,  the  theory  assumes  that  by  refraction  or 


Fig.  134. 

reflection,  all  these  vibrations  are  changed  into  two  sets, 
one  in  a  horizontal  plane,  B  (Fig.  134),  and  the  other  in  a 
vertical  plane,  C  (Fig.  134).  This  change  is  what  is  called 
POLARIZATION.  The  tourmaline  plate,  or  the  plate  of  glass, 
will  let  one  of  these  sets  of  vibrations  pass  through  it  only 
when  in  certain  positions,  owing  to  some  peculiar  arrange* 


220  NATURAL  PHILOSOPHY. 

ment  of  its  molecules,  but  when  in  position  to  cut  off  one 
set  it  allows  the  other  to  pass  freely. 

Effects  of  Polarization.  —  When  a  thin  plate  of  mica, 
or  other  doubly  refracting  medium,  is  put  at  O,  in  the  polari- 
scope  (Fig.  133),  the  two  beams  emerging,  ~by  interfering, 
produce  most  beautiful  colors.  When  seen  in  certain  direc- 
tions, colored  rings  of  surprising  beauty,  with  a  black  cross, 
appear.  The  form  and  arrangement  of  these  rings  differ  in 
different  crystals  —  a  fact  of  much  interest  to  the  mineralo- 
gist. 

Some  substances  have  the  power  to  change  the  position 
of  the  plane  of  vibration,  in  a  ray  of  polarized  light.  Thus 
if  the  analyzer  (Fig.  133)  is  turned  so  that  the  polarized 
light  is  turned  off,  a  thin  plate  of  quartz  at  O  will  cause 
the  ra}~  to  re-appear.  In  this  case  suppose  the  vibrations  to 
be  in  the  vertical  plane,  and  that  the  anatyzer  is  turned  to 
the  right  just  10°  ;  the  quartz  must  bend  the  plane  of  vibra- 
tion 10°  to  the  right  also,  in  order  that  the  ray  may  pass. 
This  is  called  ROTARY  polarization. 

A  great  number  of  liquids  have  this  power.  Some  of 
them  turn  the  plane  to  the  right ;  such  is  a  solution  of  cane- 
sugar  :  others  turn  the  plane  to  the  left ;  such  is  a  solution 
of  grape-sugar.  This  fact  is  of  great  interest  to  the  chem- 
ist, and  it  assists  the  physician  at  times  to  determine  the 
healthy  or  diseased  condition  of  the  fluids  of  the  human 
s}*stem. 

SECTION  VII. 

REVIEW. 
I.  — SUMMARY  OP    PRINCIPLES. 

The  undulations  of  the  ether,  expending  their  energy  upon 
the  e}'e  and  the  sense  of  touch,  are  recognized  as  light  and 
heat. 

These  undulations  are  transmitted  through  all  bodies  with 
greater  or  less  facility. 


NATURAL  PHILOSOPHY.  221 

Bui  when  they  strike  the  surface  of  a  second  medium  only 
a  part  of  them  enters :  another  part  is  thrown  back,  or  re- 
flected, making  the  angle  of  reflection  equal  to  the  angle  of 
incidence. 

All  effects  of  mirrors  are  explained  by  this  principle  of 
reflection. 

The  waves  which  enter  the  second  medium  are  partly 
transmitted  and  partly  absorbed. 

Those  which  are  transmitted  are  bent,  or  refracted,  mak- 
ing the  index  of  refraction  always  the  same  for  the  same 
media,  but  different  for  different  media. 

The  effects  of  lenses  are  explained  by  this  principle  of 
refraction. 

Those  waves  which  are  absorbed  in  their  passage  through 
a  body  are  transformed  into  heat  or  actinism,  expending 
their  energy  in  warming  the  body  or  in  causing  some  chemi- 
cal change. 

In  the  sunbeam  there  are  a  multitude  of  waves  of  different 
rates.  The  prism  is  able  to  separate  them,  and  when  sep- 
arated the}T  affect  the  eye  as  different  colors.  Color,  there- 
fore, depends  on  the  rate  of  the  undulation,  and  is  analogous 
to  the  pitch  of  sound. 

The  intensity  of  light  depends  on  the  amplitude  of  the 
undulations  ;  it  is  analogous  to  the  loud  ness  of  sound. 

All  the  phenomena  of  color  are  explained  on  this  principle 
of  decomposition  of  light. 

The  relation  between  wave-length,  velocit}'  in  space,  and 

y 
rate  of  the  undulation,  is  shown  by  the  formula  L  =  -£• 

For  light,  the  value  of  V  is  found  by  observations  on  the 
eclipses  of  one  of  Jupiter's  satellites,  and  also  by  experiment. 
The  value  of  L  is  found  by  experiment  with  Newton's  rings 
and  in  other  ways.  The  value  of  R  may  then  be  found  by 
the  formula. 

Velocity  of  light=186,000  miles  a  second. 

Wave-length,  for  red=. 0000266,  and  for  violet  =,00001 6 7 
inch. 


222  NATURAL   PHILOSOPHY. 

Rate  for  red=392  millions  of  millions,  and  for  violet=754 
millions  of  millions  a  second. 

Undulations  whose  rates  are  less  than  that  of  the  red  are 
recognized  only  as  heat,  and  those  with  rates  above  that  of 
the  violet  are  recognized  only  by  chemical  effects. 

Light  and  radiant  heat  may  be  polarized,  but  sound  can 
not.  This  difference  between  light  and  sound  is  explained 
by  supposing  that  the  vibrations  in  the  wave  of  light  or 
heat  are  transverse,  while  in  the  wave  of  sound  they  are 
longitudinal. 

II. —SUMMARY  OF  TOPICS. 

68.  Wave-front. — Rays  of  light. — Are   transmitted. — 
Light  moves  in  straight  lines.  — With  uniform  velocity.  — The 
law  of  intensit}7.  —  Photometry. 

69.  Reflection.  — The  law.  — Illustrations.  — Vision. 

70.  Mirrors.  —  Effect   of   plane   mirrors.  —  Of    concave 
mirrors.  — Foci.  — Effect  of  convex  mirrors. 

71.  Images  by  reflection.  —  Image   of  a  point. — Image 
by  a  plane  mirror. 

72.  Images   formed   by  a   concave   mirror.  —  Images   of 
points.  —  Of  an  object  beyond  the  center.  —  Of  an  object 
between  the  center  and  focus. — Of  an  object  between  the 
focus  and  the  mirror. 

73.  Images  by  a  convex  mirror. 

74.  Reflection  from  rough  surfaces. 

75.  Experiment   showing   refraction.  —  Definition. — The 
first  law.  — The  second  law.  — Illustrations  of  refraction. 

76.  The  index  of  refraction. — The  law.  —  Index  varies 
with  the  media. 

77.  Lenses. — Effect   of  convex  lenses. — Foci. — Effect 
of  concave  lenses. 

78.  Images  are  formed  by  lenses.  —  Explanation. 

79.  Image  of  an  object  twice  the  focal  distance.  —  Of  the 
object  farther  away.  —  Of  the  object  at  less  distance.  —  Of 
Mie  object  between  the  focus  and  the  lens. 


NATUKAL   PHILOSOPHY.  223 

80.  Image  by  concave  lens. 

81.  Prisms. — Refract   light. — Also  decompose  light. — 
Recombination  of  the  colors. 

82.  A  pure  spectrum.  — The  spectroscope.  — Fraunhofer's 
lines.  —  The  bright  lines.  —  Spectrum  analysis.  —  Invisible 
parts  of  the  spectrum,  heat.  —  Another  experiment,  chem- 
ism.  —  The  energy  of  the  sunbeam. 

83.  The  equal  diffusion  of  heat.  — Transmission  of  heat. 

—  Depends     on     temperature.  —  Nature.  —  Condition    of 
surface. 

84.  The  primary  rainbow.  —  Red  on  the  outside.  —  Colors 
in  form  of  an  arch.  —  The  secondary  bow. 

85.  The  color  of  bodies.  —  The  color  of  the  sky. — The 
color  of  the  clouds. 

86.  Sound  and  light  alike.  — Interference  of  sound.  — Of 
light.  —  The    conditions.  —  Wave-lengths   of  light.  —  The 
measurement.  —  Color  depends  on  rapidity  of  vibration.  — 
Diffraction.  — Explanation.  — Illustrations. 

87.  The  microscope.  —  Compound.  — The  telescope,  Gal- 
ileo's. —  The  astronomical.  —  The  terrestrial.  —  Reflectors. 

—  The   Herschellian.  —  The   magic-lantern. — The  camera- 
obscura.  — The  e3~e. 

88.  Double   refraction.  —  Both   beams   are   polarized.  — 
Polarizing  by  reflection.  — Polariscopes.  —  Theory  of  polari- 
zation. —  Effects. 


224  NATURAL   PHILOSOPHY. 


CHAPTER  VIII. 
ON  ELECTRICAL  ENERGY. 


SECTION   I. 
ON  FRICTIONAL  ELECTRICITY. 

89.  Electricity  ma}'  be  produced  by  friction.  The  elec- 
trical machine  is  an  apparatus  for  this  purpose.  It  ma}'  be 
detected  by  instruments  called  electroscopes,  showing  its 
action  in  two  ways,  —  by  attraction  and  repulsion.  Its 
intensity  may  be  measured  by  instruments  called  electrome- 
ters. It  is  governed  by  two  laws  :  — 

1st,  Electricities  of  the  same  kind  repel  each  other,  of 
different  kinds  attract. 

2d,  The  force  of  the  attraction  or  repulsion  is  inversely 
as  the  square  of  the  distance  between  them.  (G.  704,  711, 
714;  A.  928-931.) 

Electricity  produced  by  Friction.  —  If  a  well-dried 
glass  tube  be  thoroughly  rubbed  with  a  flannel  cloth,  it  will 
be  found  to  have  new  and  curious  properties.  Hold  it  near 
the  face,  and  a  feeling  will  be  experienced  as  if  a  gentle 
breeze  were  blowing  against  the  cheek ;  bring  it  nearer,  and 
perhaps  a  prickling  sensation  will  be  felt,  and  it  may  be 
that  a  crackling  sound  will  at  the  same  time  be  heard ;  or 
approach  it  toward  some  very  light  substances,  such  as  deli- 
cate bits  of  loose  cotton,  and  the}'  will  rush  toward  it  (see 
Fig.  135),  and  remain  for  a  little  time  clinging  to  it.  These 
various  effects  show  the  presence  of  electricity :  the  friction 
of  the  flannel  upon  the  glass  has  produced  it. 


NATURAL  PHILOSOPHY. 


225 


The  Electrical  Machine.  —  The  electrical  machine  is  an 
apparatus  for  producing  electricity  by  friction.  It  is  rep- 
resented in  Fig.  136.  Its  principal  parts  are,  1st,  a  body 


Fig.  135. 

upon  whose  surface  electricity  is  to  be  evolved ;  2d,  the 
rubber  b}7  the  friction  of  which  electricity  is  produced  ;  and, 
3d,  the  conductor  on  which  the  electricity  may  be  accumu- 
lated. In  the  form  shown  by  the  figure,  the  first  of  these 
parts  consists  of  a  thick  glass  plate  P,  to  be  turned  by  a 
crank.  The  rubber  R  is  made  of  leather,  covered  with  an 
amalgam  made  of  mercury,  tin,  and  zinc.  Two  such  pieces 
of  leather  are  pressed,  one  against  each  side  of  the  plate, 
by  means  of  a  brass  clamp,  which  is  supported  upon  a  glass 
pillar.  The  conductor,  or  as  usually  called  the  prime  con- 
ductor, C,  is  a  brass  ball,  or  a  cylinder  with  rounded  ends, 
mounted  on  a  glass  support.  Connected  with  the  prime 
conductor,  is  a  brass  fork  F,  one  prong  of  which  is  on  each 
side  of  the  plate,  with  man}'  sharp  projecting  points  reaching 
toward  the  glass. 


226 


NATURAL  PHILOSOPHY. 


Its  Action.  —  By  turning  the  crank,  the  friction  of  the 
rubber  upon  the  plate  evolves  electricity,  which  remains 
upon  the  surface  of  the  glass  until  it  is  brought  arcund  to 
the  fork,  and  the  prime  conductor  is  thrown  into  the  same 
electrical  condition.  We  shall  soon  see  how  this  action  is 
explained  on  the  principle  of  induction.  The  glass  support 
prevents  the  electricity  from  leaving  the  conductor.  When 
the  machine  is  in  operation  the  rubber  is  connected  with  the 
floor  by  a  chain.  All  parts  of  the  machine  must  be  free 
from  dust  and  thoroughly  dry. 

When  a  machine  of  this  kind,  of  medium  size,  is  in  suc- 
cessful operation,  the  effects  of  the  glass  tube  are  experi- 


Fig.  136. 

enced  in  a  far  greater  degree.  The  face  or  the  back  of  the 
hand  will  feel  the  breezy  or  prickling  sensation  at  a  distance 
of  several  inches  from  the  conductor ;  all  light  bodies  held 
near  it  immediately  fry  to  its  surface  ;  and,  if  the  knuckle  or 
a  brass  ball  be  brought  near,  bright  and  zigzag  sparks  may 


NATURAL 


227 


be  drawn  through  a  distance  of  from  one  to  two  inches,  the 
light  being  accompanied  by  a  sharp  report. 

Electricity  detected  by  Electroscopes.  —  When  the 
electricity  is  feeble,  there  should  be  some  more  convenient 
way  of  showing  its  presence.  Any  instrument  for  this 
purpose  is  called  an  ELECTROSCOPE.  The  simplest  form 
is  called  the  pith-ball  electroscope.  It  consists  (see  Fig. 
137)  of  a  ball  of  pith  from  the  corn-stalk,  or  elder,  hung  by 


Fig.  137. 

a  slender  silk  thread  from  a  glass  support.  This  little  ball 
will  instantly  announce  the  presence  of  electricity  by  moving 
toward  the  body  which  contains  it,  and  after  a  moment 
leaping  away  again. 

Two  Opposite  Actions.  —  In  this  experiment  the  elec- 
tricity shows  its  presence  both  b}r  attraction  and  repulsion. 
If  the  pith-ball  of  the  electroscope  be  brought  near  to  the 
prime  conductor  of  the  electrical  machine,  it  will  fly  toward 


228  KATtJfcAL  PHILOSOPHY. 

it,  but,  on  coming  in  contact  with  it,  will  as  instantly  leap 
away  again. 

Now,  rub  a  glass  rod  with  flannel,  and  hold  it  near  the 
pith-ball  which  has  been  repelled  by  the  conductor ;  the  glass 
rod  will  also  repel  it ;  but,  if  a  stick  of  sealing-wax  be  used 
in  place  of  the  glass  tube,  the  pith-ball  will  be  strongly  at- 
tracted. Notice,  that  the  pith-ball  is  repelled  by  the  elec- 
tricity of  glass,  and  attracted  by  the  electricity  of  sealing-wax. 
It  is  thus  seen  that  the  electricities  of  glass  and  sealing-wax 
are  not  alike.  To  distinguish  them  from  each  other,  that 
which  is  produced  on  glass  by  the  friction  of  flannel  is  called 
positive  ( + )  electricity ;  that  produced  upon  sealing-wax  is 
called  negative  (  —  )  electricity. 

It  is  found  to  be  impossible  to  develop  one  of  these  condi- 
tions without  the  other  also.  The  positive  always  appears 
on  one  of  the  bodies  rubbed  together,  and  the  negative  upon 
the  other. 

The  Law.  —  We  have  seen  that  positive  electricity  is 
produced  by  friction  on  glass,  and  that  the  opposite  force  is 
evolved  by  friction  on  sealing-wax.  Now  let  two  pith-balls 
-be  suspended  by  silk  threads  so  as  to  be  in  contact.  Thor- 
oughly rub  the  glass  tube  ;  bring  it  in  contact  with  the  balls  ; 
the}'  both  receive  positive  electricity  from  the  tube,  and  it 
will  be  found  that  the}'  will  no  longer  remain  in  contact.  We 
learn"  from  this  experiment  that  two  bodies  with  the  same 
kind  of  electricity  repel  each  other. 

Again :  let  the  sealing-wax  be  thoroughly  rubbed  and 
brought  near  to  the  two  pith-balls  while  the}'  are  repelling 
each  other,  and  they  will  both  fly  toward  it.  We  learn  from 
this  experiment  that  bodies  with  different  kinds  of  electricity 
attract  each  other.  . 

Bodies  in  the  same  electrical  condition  repel  one  another; 
in  opposite  conditions  they  attract. 

Application.  —  This  law  furnishes  an  easy  test  by  which 
to  find  out  which  kind  of  electric  force  is,  in  any  case,  pro- 
duced. Is  the  prune  conductor  of  the  electrical  machine 


NATtTfcAL  PHILOSOPHY. 

positive  or  negative?  To  decide  the  .question,  rub  the  glass 
tube ;  bring  it  in  contact  with  the  pith-ball  of  the  electro- 
scope ;  the  electricity  of  the  ball  is  thus  known  to  be  posi- 
tive. Now,  bring  it  near  the  prime  conductor  of  the  machine 
in  operation  ;  it  is  repelled.  The  electricity  of  the  conductor 
is  positive.  The  electricity  of  the  rubber  is  negative,  be- 
cause, if  the  chain  be  removed,  and  the  electrified  pith-ball 
be  brought  near  the  brass  mounting  of  the  rubber,  it  will 
be  attracted. 

90.  A  charged  or  electrified  bod}',  acting  through  a  non- 
conductor upon  an  insulated  conductor,  polarizes  it.  This 
action  is  called  induction.  (G.  722-726,  728.) 

A  charged.  Body. — Whenever  by  friction,  electricity  is 
developed  upon  the  surface  of  a  body,  the  body  is  said  to 
be  electrified  ;  and  if,  by  bringing  another  bod}'  in  contact 
with  it,  electricity  is  imparted,  the  body  which  receives  it  is 
said  to  be  charged.  Thus  the  glass  tube,  when  rubbed, 
becomes  electrified;  the  pith-ball  of  the  electroscope,  coming 
in  contact  with  the  glass,  takes  electricity  from  it,  and  be- 
comes charged. 

A  Non-Conductor. — rSome  bodies  allow  electricity  to 
pass  freely  over  their  surfaces  ;  such  bodies  are  called  CON- 
DUCTORS :  others  will  not  allow  electricity  to  pass  freely  over 
them ;  these  are  called  NON-CONDUCTORS.  If  a  brass  rod 
be  held  in  contact  with  the  prime  conductor  of  a  machine, 
it  will  be  found  impossible  to  charge  it ;  a  glass  rod  held  in 
the  same  way  will  not  'prevent  the  charge  from  accumulat- 
ing. The  brass  allows  the  electricity  to  pass  into  the  per- 
son ;  the  glass  does  not :  brass  is  a  conductor ;  glass  is  a 
non-conductor.  The  metals,  as  a  class,  are  good  conductors. 
Beside  glass,  we  notice  silk,  India  rubber,  and  dry  air,  as 
being  among  the  best  non-conductors. 

Potential.  —  The  electric  condition  of  the  earth  is  the 
standard  with  which  to  compare  the  electrfc  conditions  of 
other  bodies.  In  the  earth  we  suppose  the  -f-  and  —  electri- 


2SO  NATtTRAL  PHILOSOFHt. 

cities  to  be  just  balanced  :  the  electric  power  is  zero.  The 
term  potential  is  used  in  comparing  electric  conditions. 
When  the  condition  is  the  same  as  that  of  the  earth,  the 
potential  is  zero. 

High  and  Low  Potential.  —  When  the  electricity  at  any 
place  is  greatly  in  excess  of  that  in  the  earth,  it  is  described 
as  a  high  potential.  A  less  and  less  excess  is  spoken  of  as 
a  lower  and  lower  potential.  And,  when  the  electricity  falls 
below  that  of  the  earth,  the  potential  is  negative. 

The  potential  of  a  bod}'  is  the  difference  between  its 
electric  power  and  that  of  the  earth  in  its  neighborhood. 

Electro-Motive  Force.  —  Now  remember  that  electricity 
always  passes  from  a  place  of  high  to  one  of  lower  poten- 
tial, as  surely  as  water  will  run  from  a  high  to  a  lower  level. 
And  just  as  we  speak  of  the  force  of  gravity  as  the  cause 
of  the  flow  of  water,  so  we  speak  of  electro-motive  force  as 
that  which  urges  electricity  along  over  a  conductor. 

Electro-motive  force  may  be  also  described  as  the  differ- 
ence in  the  potentials  of  two  places. 

An  insulated  Body.  —  Whenever  a  bod}T  is  quite  sur- 
rounded by  non-conductors,  it  is  said  to  be  insulated.  The 
conductor  of  the  machine  is  insulated  by  resting  upon  a 
glass  support.  A  body  which  is  not  insulated  can  not  be 
charged. 

A  charged  Body  polarizes  an  insulated  Conductor. 
—  A  bod}*  is  said  to  be  polarized  when  the  two  opposite 
electricities  both  exist  upon  its  surface.  To  illustrate  this 
important  condition,  let  an  insulated 
metallic  ball  be  connected  with  the 
prime  conductor  of  the  electrical  ma- 
chine, and  let  a  small  insulated  con- 
ductor be  placed  near  it  (see  Fig. 
138).  When  the  ball  is  charged,  the 
motion  of  the  pith-balls  fastened  to 

the  small  conductor  shows  that  it  is  also  electrified,  and,  if 
its  electricity  be  tested,  it  will  be  found  to  be  positive  at  one 


NATURAL   PHILOSOPHY.  231 

end  and  negative  at  the  other.  Both  electricities  are  devel- 
oped upon  its  surface  at  the  same  time,  and  the  body  is  said 
to  be  polarized.  The  action  of  the  ball,  by  which  this  body 
is  polarized,  is  called  INDUCTION. 

If  we  examine  the  condition  of  the  polarized  body  more 
carefully,  we  find  that  in  the  end  next  to  the  ball  there  is 
negative  electricity,  and  in  the  distant  end  there  is  positive 
electricity.  This  is  always  true :  when  a  body  is  electrified 
by  induction,  the  end  or  side  nearest  the  charged  body  is  al- 
ways in  a  condition  opposite  to  that  which  develops  it. 

The  insulated  conductor  is  electrified  only  when  near  to 
the  ball.  Let  it  be  moved  away,  and  the  pith-balls  drop. 

To  charge  it. — But  if,  when  the  conductor  is  polarized, 
we  touch  it  with  the  finger,  the  electricity  which  is  like  that 
of  the  charged  bod}'  will  pass  off,  and  the  entire  surface 
will  remain  charged  with  the  opposite  kind.  It  will  remain 
charged,  even  when  taken  beyond  the  influence  of  the  body 
which  polarized  it. 

91.  A  series  of  insulated  conductors,  placed  end  to  end, 
near  each  other,  ma}'  be  all  polarized  by  bringing  a  charged 
body  near  to  one  of  them.  Faraday's  theory  explains  in- 
duction by  supposing  the  molecules  of  a  body  to  be  polar- 
ized, one  by  another,  in  the  same  way.  (G.  724,  726,  729.) 

A  Series  of  Conductors  may  be  polarized.  —  Let    a 

number  of  small  insulated  conductors  be  placed  end  to  end, 
near  together,  with  one 
end  of  the  first  one  near 
to  a  brass  ball  connected 
with  the  prime  conductor 
of  the  machine  (see  Fig. 
139).  The  motion  of  the  Fig>  139' 

pith-balls  will  show  that  they  are  all  polarized.  The  effect 
will  be  greater  if  another  brass  ball,  connected  with  the  rub- 
ber of  the  machine,  is  placed  at  the  other  end  of  the  series. 
The  positive  and  negative  electricities  are  on  opposite  ends 


232  NATURAL   PHILOSOPHY. 

of  each  conductor.     All  the  ends  toward  the  positive  ball  are 
negative  ;  all  the  ends  in  the  other  direction  are  positive. 

Faraday's  Theory  of  Induction.  —  Now,  the  molecules 
of  one  of  these  conductors  are  as  truly  separate  bodies  as 
the  conductors  themselves  ;  and,  as  one  electrified  conductor 
may  polarize  another,  so  one  of  these  molecules,  acting 
through  the  minute  distance  between  them,  may  polarize 
another.  This  polarizing  influence  passes  from  one  molecule 
to  another,  until  all  the  molecules  of  the  body  are  thrown 
into  this  condition,  each  molecule  having  opposite  electrici- 
ties on  its  opposite  sides. 

Difference  between  Conductors  and  Non-Conductors. 
—  The  theory  goes  further,  and  supposes  that  the  molecules 
of  conductors  discharge  their  electricity  easily  into  one 
another,  while  those  of  non-conductors  do  not.  For  this 
reason,  the  molecules  of  the  air  between  the  charged  ball 
and  the  end  of  the  conductor  are  polarized,  and  retain  their 
electricities,  while  the  molecules  of  the  conductors,  as  fast 
as  they  are  polarized,  give  their  electricit}'  to  their  neighbors. 
The  positive  electricity  given  from  one  to  another,  in  one 
direction,  accumulates  at  one  end  of  the  conductor  ;  the 
negative,  given  from  one  to  another  in  the  other  direction, 

accumulates  at  the  other  end. 

Polarization  precedes  Elec- 
trical Attraction.  —  The  first  ac- 
tion of  an  electrified  body  is  to 
polarize  every  other  in  its  neighbor- 
hood. The  attraction  of  pith-balls 
or  cotton  (Figs.  137  and  135)  by 
the  excited  glass  takes  place  after 
they  have  been  polarized. 

Illustration.  —  Fig.  140  shows 
a  chime  of  bells,  which  are  to  be 

rung  by  electricny.     The  two  out- 
Pig.  140.  side   be|ls   are   fastene(j  b     metaj 


chains  to  a  rod  of  metal  which  hangs  from  the  end  of  the, 


NATURAL  PHILOSOPHY. 


238 


prime  conductor  of  an  electrical  machine.  The  middle  bell 
is  hung  by  a  silk  thread,  and  has  a  chain  passing  from  it 
to  the  floor.  Finalhr,  notice  two  little  balls  of  metal  between 
the  bells  ;  these  balls  are  hung  by  silk  threads  also.  When 
the  machine  is  in  operation,  these  little  balls  will  fly  back  and 
forth  and  ring  the  bells  merrily. 

Now  when  the  outside  bells  are  -f,  they  polarize  the  balls. 
The  sides  of  the  balls  nearest  the  bells  are  — ,  and  hence 
bells  and  balls  attract.  The  balls  then  strike  the  bells, 
become  -f-  b}'  contact,  and  balls  and  bells  repel.  The  middle 
bell  is  polarized  —  :  the  +  balls  strike  it,  and  discharge 
their  electricit}',  which  passes  off  into  the  earth  by  the  chain. 
This  series  of  actions  is  repeated  over  and  over  again. 
Polarization,  attraction,  charge,  repulsion,  discharge,  follow 
repeated!}'  in  regular  order. 

Iii  the  Electrical  Machine.  —  We  are  now  prepared  to 
see  how  the  prime  conductor  of  the  electrical  machine  be- 
comes charged.  The  glass  plate  near  the  fork  is  electrified 
with  -f  electricity.  It  polarizes  the  prime  conductor  near  it. 
The  —  electricity  which  accumulates  in  the  adjacent  end  is 
discharged  from  the  points  of  the  fork  upon  the  surface  of 
the  glass,  and  this  leaves  the  conductor  charged  with  + 
electricity. 

92.  The  Holtz 
machine  is  an  in- 
strument  with 
which  to  develop 
electricity  by  the 
continuous  induc- 
tive action  of  an 
electrified  body. 
(G.  736.) 

Description.  —  Fi»- 141- 

One  form  of  the  Holtz  machine  is  shown  in  Fig.  141. 
Two  thin  glass  plates  are  insulated,  as  near  together  as 


234  NATURAL  PHILOSOPHY. 

possible  without  touching.  The  larger  plate  is  stationary, 
while  the  smaller  one  may  be  rotated  very  swiftly  by  a 
wheel  and  pulley.  Two  windows  are  cut  in  the  stationary 
plate,  and  two  paper  sectors,  called  armatures,  are  ce- 
mented against  the  back  side  of  it,  on  opposite  sides  of  the 
windows.  From  the  edge  of  each  sector  a  set  of  points 
project  into  the  window.  Opposite  these  points,  and  sep- 
arated from  them  by  the  revolving  plate,  are  two  brass 
combs.  These  combs  are  also  connected  each  with  a  brass 
ball  in  front  of  the  machine,  and  these  balls  are  on  sliding 
rods  so  that  the  distance  between  them  may  be  changed  at 
will.  Each  comb  and  ball  are  in  connection  with  the  in- 
side of  a  Leyden-jar,  which  we  shall  very  soon  describe, 
while  the  outsides  of  the  jars  are  joined  by  a  chain. 

Its  Action. — To  put  the  machine  in  action,  one  of  the 
ai-matures  is  first  electrified  by  bringing  an  electrified  piece 
of  vulcanite  against  it,  and  then  turning  the  wheel.  In  a 
few  seconds  the  difference  of  potential  in  the  two  jars  be- 
comes so  great  that  they  discharge  in  a  series  of  vivid  sparks 
leaping  between  the  balls  in  front. 

Explanation.  —  The  -f-  armature  polarizes  the  comb  in 
front  of  it,  and  attracts  the  —  electricity  which  is  projected 
from  its  points  upon  the  surface  of  the  revolving  plate,  leav- 
ing the  comb  charged  with  +  electricity.  The  other  arma- 
ture is  — ,  and  by  a  similar  induction  causes  a  —  charge  in  the 
other  comb.  These  +  and  —  charges  accumulate  in  the  Ley- 
den-jars  until  they  discharge  between  the  balls.  Such,  in  a 
general  way,  is  the  theoiy  of  the  Holtz,  but  the  details  of 
its  action  are  complex  and  puzzling.  For  a  full  explana- 
tion the  student  may  consult  a  larger  work  on  physics. 

93.  The  Leyden-jar  is  an  apparatus  for  accumulating  elec- 
tricity by  induction.  It  may  be  charged  by  bringing  one  of 
its  coatings  in  contact  with  a  charged  body,  the  other  being 
in  contact  with  conductors.  It  may  be  discharged  by  mak- 
ing a  conducting  communication  between  its  two  coatings. 


HATURAL  PHILOSOPHY. 


235 


Pig.  142. 


The   Leyden  battery  consists   of  several  Leyden-jars   con- 
nected.    (G.  743,  757,  758  ;  A.  945.) 

The  Leyden- Jar.  —  The  Ley  den-jar  consists  of  a  glass 
jar,  coated  both  inside  and  outside  with  tin-foil,  to  within 
a  few  inches  of  the  top,  and  provided  with 
a  cover  of  hard  dry  wood,  through  which 
passes  a  brass  rod,  with  a  ball  upon  its  upper 
end,  and  a  chain  reaching  from  its  lower  end 
to  the  bottom  of  the  jar. 

It  will  be  seen  by  this  description,  that  in 
this  instrument  there  are  two  conducting  sur- 
faces, separated  from  each  other  by  a  non- 
conductor. 

Various  Forms.  —  This  idea  may  be  em- 
bodied in  a  variety  of  forms,  any  one  of 
which  will  act  on  the  principle  of  the  Leyden- 
jar.  Thus  a  pane  of  glass,  coated  with  tin- 
foil on  both  sides,  to  within  a  little  distance  of  the  edge  all 
around,  has  the  essential  parts  of  the  Leyden-jar.  A  glass 
goblet  partly  full  of  water,  and  grasped  by  the  hand,  illus- 
trates the  same  idea :  the  glass,  a  non-conductor,  separates 
two  conducting  surfaces  —  the  water  on  the  inside,  and  the 
hand  upon  the  outside. 

It  may  be  charged.  —  By  bringing  the  ball  of  the  Ley- 
den-jar  in  contact  with  the  prime  conductor  of  the  machine, 
positive  electricit}'  passes  into  the  inside  coating.  This  posi- 
tive electricity  polarizes  the  glass  and  the  outside  coating, 
causing  its  surface  next  the  glass  to  be  negative,  and  the 
other  to  be  positive.  If  in  contact  with  a  conductor,  this 
positive  electricity  will  pass  off,  and  thus  leave  the  outside 
coating  permanently  charged  with  negative  electricity. 
When  by  this  action  the  two  coatings  have  opposite  elec- 
tricities, the  jar  is  said  to  be  charged.  It  may  be  removed 
from  the  prime  conductor,  and  remain  charged,  because  the 
two  electricities  attract  each  other  without  a  chance  for  dis- 


236  NATURAL   PHILOSOPHY. 

charge  through  the  glass.  The  jar  may  be  handled  without 
danger,  if  care  be  taken  not  to  touch  the  ball  and  the  out- 
side at  the  same  time. 

The  jar  is  charged  with  positive  electricity  when  the  in- 
side is  positive  :  it  is  charged  with  negative  electricity  when 
the  inside  is  negative. 

It  may  be  discharged.  —  The  difference  of  potential 
between  the  inside  and  outside  is  very  great,  and,  when  a  con- 
ducting communication  is  made  between  the  two  coatings  of 
the  jar,  the  electricity  passes  until  equilibrium  is  restored, 
and  the  jar  is  said  to  be  discharged.  The  conducting  com- 
munication may  be  made  in  many  waj's.  The  discharger  is 
a  convenient  instrument  for  the  purpose.  It  consists  of  two 
bent  brass  arms,  with  a  ball  upon  one  end  of  each,  the  other 
ends  being  fastened  by  a  joint  to  a  glass  handle.  Taking 
hold  of  the  glass  handle,  bring  one  ball  in  contact  with  the 
outside  of  the  jar,  and  the  other  near  to  the  knob  ;  a  bright 
spark  and  a  sudden  report  announce  the  discharge. 

The  coated  glass  plate  and  the  goblet  of  water,  mentioned 
before,  ma}*  be  charged  and  discharged  in  the  same  way  as 
a  Leyden-jar.  To  charge  the  goblet,  for  example,  let  a 
chain  from  the  prime  conductor  of  the  machine  hang  into 
the  water ;  grasp  the  outside  of  the  glass  while  the  machine 
is  in  operation.  Positive  electricity  will  be  given  to  the 
water ;  negative  electricity  will  be  induced  upon  the  hand, 
and  the  goblet  is  thus  charged.  Now  with  the  other  hand 
try  to  remove  the  chain :  the  moment  the  chain  is  touched, 
a  slight  shock  will  be  felt,  announcing  the  discharge  which 
occurs. 

The  Leyden  Battery-  —  The  larger  the  surface  of  the 
coatings  of  the  jar,  the  more  powerful  will  be  the  charge 
accumulated.  We  can  obtain  a  larger  surface  by  using  a 
larger  jar,  or  it  may  be  done  by  taking  several  small  ones 
and  joining  their  surfaces  by  conductors.  In  the  last  case, 
the  Leyden  battery  will  be  formed.  When  the  inside  sur- 
faces are  all  connected  by  conductors  reaching  from  knob  to 


NATUKAL   PHILOSOPHY.  237 

knob,  and  the  outsides  all  joined  by  standing  the  jars  on  a 
metallic  surface,  the  battery  may  be  charged  and  discharged 
as  a  single  jar.  It  is  equivalent  to  a  single  jar  large  enough 
to  have  the  same  extent  of  surface. 

94.  The  electricity  of  the  atmosphere  is  of  the  same 
nature  as  that  produced  by  friction.  Lightning  is  the  dis- 
charge of  oppositely  charged  clouds,  illustrating,  on  a  grand 
scale,  the  action  of  a  Leyden-jar. 

Electricity  of  the  Atmosphere.  —  The  atmosphere  is 
very  generally  in  an  electrified  condition.  This  may  be 
shown  by  raising  a  metallic  rod  to  a  considerable  height 
above  the  ground,  having  an  electroscope  fastened  to  its 
lower  end,  which  should  be  insulated.  A  sensitive  electro- 
scope will  usually  indicate  positive  electricity,  its  intensity 
increasing  as  the  air  from  which  it  is  drawn  is  higher.  In 
its  ordinary  state,  the  electricity  of  the  atmosphere  is  always 
positive  :  stronger  in  winter  than  in  summer,  and  during  the 
day  than  the  night.  In  cloudy  weather  the  electrical  state 
is  uncertain,  sometimes  changing  from  positive  to  negative 
and  back  again  in  a  few  minutes.  On  the  approach  of  a 
thunderstorm  these  changes  follow  each  other,  at  times,  with 
remarkable  swiftness. 

It  is  of  the  same  Nature  as  frictional  Electricity  0 — 
The  bright  flash  and  loud  report  which  announce  the  dis- 
charge of  a  Leyden-jar  or  battery  can  not  have  failed  to 
remind  one  who  has  observed  them,  of  the  brighter  flash  and 
louder  report  of  atmospheric  lightning  and  thunder.  These 
grand  and  sometimes  awful  displays  of  electricity  are  caused 
by  the  same  agent  which,  produced  on  a  glass  tube,  lightly 
pricks  the  cheek  or  attracts  a  pith-ball. 

To  Dr.  Franklin  belongs  the  immortal  honor  of  proving 
the  identity  of  electricity  and  lightning.  A  kite  was  the 
simple  instrument  which  he  employed.  Having  made  a 
kite  by  stretching  a  silk  handkerchief  over  two  sticks  in 
the  form  of  a  cross,  he  went  out  into  a  field,  accompanied 


238  NATURAL   PHILOSOPHY.. 

only  by  his  son  ;  raised  his  kite  ;  fastened  a  key  to  the  lower 
end  of  its  hempen  string ;  insulated  it  by  fastening  it  to  a 
post  b}'  means  of  a  silk  cord,  and  anxiously  awaited  the 
approaching  storm.  A  dense  cloud,  apparently  charged  with 
lightning,  soon  passed  over  the  spot  where  he  stood,  without 
causing  his  apparatus  to  give  an}*  sign  of  electricnVy.  He 
was  about  to  give  up  in  despair,  when  he  caught  sight  of 
some  loose  fibers  of  the  hempen  cord  bristling  up  as  if  re- 
pelled. He  immediately  presented  his  knuckle  to  the  ke}r, 
and  received  an  electric  spark.  The  string  of  his  kite  soon 
became  wet  with  the  falling  rain ;  it  was  then  a  better 
conductor,  and  he  was  able  to  obtain  an  abundance  of  sparks 
from  the  key.  By  this  experiment  he  furnished  a  decisive 
proof  of  the  identity  of  lightning  and  electricit}'. 

Lightning  is  the  Discharge  of  oppositely  Charged 
Clouds.  —  Clouds  are  often  charged  with  electricity.  When 
two  of  them,  with  opposite  kinds  of  electricity,  come  near 
enough  together,  they  will  act  like  the  two  charged  coatings 
of  the  Leyden-jar,  the  air  between  them  being  a  non-con- 
ductor like  the  glass.  When  the  charge  rises  high  enough, 
a  discharge  takes  place  ;  the  spark  of  the  discharge  being  a 
flash  of  lightning,  and  its  report  a  thunder-peal.  Consider- 
ing the  large  extent  of  cloud  surfaces  discharged,  we  need 
not  be  surprised  at  the  magnitude  of  the  spark,  nor  at  the 
deep  intensit}r  of  the  sound. 

When  the  discharge  is  not  hidden  by  clouds,  we  can  trace 
the  whole  length  of  the  spark,  and  we  witness  chain-light- 
ning :  but  at  other  times  the  spark  is  behind  the  clouds  ;  we 
see  only  the  light  of  the  discharge  spread  over  the  surface 
of  the  clouds,  and  this  gives  rise  to  what  is  called  sheet- 
lightning. 

At  times  the  earth  and  a  cloud  are  the  two  charged  sur- 
faces, and  a  discharge  takes  place  between  them.  Such 
discharges  are  the  source  of  danger  to  life  and  property. 
Animals,  trees,  buildings,  all  these  are  better  conductors 
than  air,  and  electricity  always  chooses  the  best  conductors 


NATURAL   PHILOSOPHY.  239 

in  its  passage.  In  going  from  a  cloud  to  the  earth  it  takes 
these  bodies  in  its  way  ;  animals  are  often  killed,  trees  shat- 
tered, and  buildings  torn  to  pieces  or  set  on  fire. 

95.  A  bod}*  having  points  projecting  from  its  surface  can 
not  be  charged  even  when  insulated.  Or,  if  a  pointed  con- 
ductor be  held  toward  its  surface,  it  will  prevent  a  charge 
from  accumulating.  Upon  this  principle,  buildings  are  pro- 
tected from  the  effects  of  lightning  by  lightning-rods. 

The  effect  of  Points.  —  It  is  found  to  be  impossible 
to  charge  a  conductor  when  there  are  sharp  points  on  its 
surface,  or  held  near  to  it.  Fasten  a  pointed  wire  to  the 
prime  conductor  of  the  electrical  machine,  and  the  sparks, 
which  before  could  be  drawn  from  it  in  abundance,  cease 
altogether,  and  even  pith-balls  fail  to  detect  the  presence  of 
the  force.  Or  take  the  pointed  wire  in  the  hand,  and  present 
its  point  to  the  prime  conductor,  within  a  few  inches  of  its 
surface ;  not  a  spark  can  be  drawn  from  it,  nor  will  the  pith- 
balls  show  either  attraction  or  repulsion.  The  discharge  is 
silently  effected  by  the  air  in  front  of  the  points.  Its  mole- 
cules become  polarized,  and  are  first  attracted  to  the  point 
and  then  repelled.  On  coming  in  contact  with  the  point, 
the}7  take  electricity  from  it,  and  move  away :  others  being 
polarized  are  attracted,  receive  electricity,  and  pass  away. 
Thus  the  electricity  of  the  body  is  silently  carried  off  from 
the  point.  That  such  currents  of  air  do  really  exist,  may 
be  proved  by  various  experiments.  If,  for  example,  the 
cheek,  or  the  back  of  the  hand,  be  held  near  to  the  point, 
the  breeze  will  be  felt ;  or,  if  the  small  flame  of  a  lighted 
taper  be  held  just  in  front  of  the  point  on  the  prime  con- 
ductor, it  will  be  blown  away  from  it,  and  may  even  be 
extinguished. 

Lightning-Rods.  —  We  have  seen  that  because  build- 
ings are  better  conductors  of  electricity  than  air,  they  are 
liable  to  injury  from  strokes  of  lightning.  But,  since  pointed 
conductors  silently  discharge  the  force  from  a  charged  body, 


240  NATUBAL  PHILOSOPHY. 

why  not  disarm  the  cloud  of  its  lightning  by  the  use  of 
pointed  metallic  rods?  This  question  was  no  sooner  sug- 
gested to  the  practical  mind  of  Franklin,  than  a  trial  was 
made,  which  verified  his  bold  conjecture. 

Conductors  for  the  purpose  of  protecting  buildings  from 
the  effect  of  lightning  are  called  lightning-rods.  The}r 
should  be  made  of  metallic  rods,  pointed  at  the  upper  end, 
reaching  several  feet  above  the  highest  part  of  the  building 
which  the}'  are  designed  to  protect,  and  downward,  without 
interruption,  into  the  ground  below  its  foundation,  far  enough 
to  be  always  in  moist  earth. 

96.  The  effects  of  frictional  electricity  are  mechanical, 
chemical,  and  physiological.  (G.  760-762,  770;  A.  949, 
951.) 

Mechanical  Effects.  —  We  have  already  had  abundant 
illustrations  of  motions  caused  by  electricit}'.  Poor  con- 
ductors are  also  pierced  or  torn  by  the  electric  discharge. 
To  illustrate  this  by  experiment,  let  the  charge  of  a  Leyden- 
jar  be  passed  through  a  piece  of  cardboard ;  the  card  will 
be  pierced  with  a  burned  or  ragged  perforation.  This  effect 
is  produced  on  a  large  scale  by  the  lightning-stroke  ;  even 
rocks  are  sometimes  shattered,  while  trees  are  often  splin- 
tered from  top  to  root,  and  their  fragments  scattered  far  and 
near  in  all  directions. 

Chemical  Effects.  —  The  chemical  effects  of  electricity 
are  shown  through  the  agency  of  the  heat  which  it  de- 
velops. To  illustrate  by  experiment :  wrap  the  ball  of  a 
Le}'den-jar  with  loose  cotton,  and  sprinkle  upon  this,  very 
finely  powdered  resin.  This  done,  charge  the  jar  power- 
fully, and  then  discharge  it  by  bringing  first  one  ball  of  the 
discharger  in  contact  with  the  outside  of  the  jar,  and  then 
the  other  a  little  above  its  hooded  knob.  The  discharge 
takes  place  through  the  resin,  and  sets  it  on  fire.  Buildings 
are  sometimes  set  on  fire  by  the  lightning-stroke. 

Physiological  Effects.  —  The  effect  of  electricity  upon 


NATURAL  PHILOSOPHY.  241 

the  human  system  is  peculiar  and  startling.  No  descrip- 
tion can  give  a  correct  idea  of  it:  it  must  be  experienced 
by  one  who  would  know  what  it  is.  Let  a  person  place 
one  hand  upon  the  outside  surface  of  a  lightly  charged 
Lej'den-jar,  and  with  the  other  hand  touch  its  knob.  He 
will  find  that  he  can  no  longer  control  his  muscles :  his 
hands  are,  on  the  instant,  suddenly  jerked,  while  a  peculiar 
and  almost  indescribable  sensation  is  felt  in  the  wrists  and 
arms. 

Many  persons  by  joining  hands  may  form  an  unbroken 
connection  between  the  two  coatings  of  the  jar,  and  all  at 
once  experience  these  effects. 


SECTION  II. 

ON  MAGNETIC  ELECTRICITY. 

97.  Magnets  are  either  natural  or  artificial,  and  may  be 
made  in  different  forms  ;  but  in  any  form  the  magnetism  is 
stronger  at  the  ends  than  in  the  middle.  The  ends  are 
called  poles.  (A.  967,  974;  G.  670,  895.) 

Magnets.  —  Bodies  that  attract  iron  in  preference  to 
other  metals  are  called  MAGNETS. 

Fragments  of  an  ore  of  iron  are  sometimes  found,  which 
have  the  properties  of  a  magnet.  Such  a  fragment  is  a 
NATURAL  MAGNET  or  LODE  STONE. 

If  a  bar  of  iron  or  steel  be  rubbed  against  a  magnet, 
it  will  become  magnetic  ;  it  will  then  be  an  artificial  magnet. 

Soft  iron  or  steel  will  lose  its  magnetic  properties  quick!}' ; 
hardened  iron  or  steel  will  retain  them. 

The  bar  magnet  is  a  straight  bar  of  steel ;  the  horseshoe 
magnet  is  a  magnet  whose  shape  is  that  of  a  horseshoe,  or 
the  letter  U  (see  Fig.  143)  ;  its  ends  are  thus  brought  near 
together.  A  piece  of  soft  iron  acro3s  the  ends,  N  S,  is 
tailed  the  armature. 


242 


NATURAL  PHILOSOPHY. 


Experiment.  —  To  illustrate  their  peculiar  preference  for 
iron,  let  some  iron-filings  be  mixed  with  some  filings  of 
brass  ;  bring  one  end  of  the  magnet 
among  the  filings,  and  on  removing 
it  great  numbers  of  the  iron  parti- 
cles will  be  seen  clinging  to  it,  while 
the  brass  particles  are  all  left  behind. 
Their  Force  is  Stronger  at 
their  Ends.  —  If  a  bar  magnet  be 
rolled  in  a  bed  of  iron-filings,  large 
clusters  of  them  will  be  found  cling- 
ing to  its  ends,  their  numbers  get- 
ting less  toward  the  middle  of  the 
bar,  where  very  few,  if  an}',  will  be 
held.  (Fig.  144.)  By  this  experi- 
ment we  learn  that  the  magnetism  is 
not  equally  distributed  over  the  sur- 
faces of  magnets,  but,  on  the  con- 
trary, that  it  is  strong  at  the  ends 
and  weak  or  neutral  in  the  middle. 
The  ends  are  called  POLES,  one  being 
a  north  pole,  the  other  a  south  pole. 

98.  Magnetism  shows  itself  both 
ig.  143.  ky  attraction  an(j  repulsion,  obe}'ing 

the  following  law :  Poles  of  like  names  repel  each  other ; 
those  of  different  names  attract. 

Attraction  and  Repulsion.  —  Iron  which  is  not  mag- 
netized will  be  attracted  equally  by  both  poles  of  a  magnet ; 
it  is  not  so  when  two  magnets  act  upon  each  other.  By  pre- 
senting the  south  pole  of  a 
magnet  to  the  north  pole  of 
another,  it  will  show  an  at- 
traction for  it,  while  the  north 

pole,  being  presented  to  the  north  pole,  will  repel  it.  Thus 
magnetism,  like  electricity  by  friction,  shows  itself  by  both 
attraction  and  repulsion. 


NATURAL  PHILOSOPHY.  248 

It  is  also  evident  from  these  experiments  that  poles  of  the 
fame  name  repel,  while  those  of  opposite  names  attract. 

99.  A  magnet,  like  a  charged  body,  will  polarize  a  bar  of 
iron  brought  near  to  one  of  its  poles,  always  inducing  mag- 
netism of  the  opposite  kind  in  the  end  next  to  it.  The 
polarizing  influence  may  extend  through  several  bars  placed 
end  to  end. 

It  is  supposed  that  eveiy  molecule  of  a  magnet  is  in  a 
polarized  state,  the  north  polarity  being  on  the  same  side 
of  them  all,  and  the  south  polarity  on  the  other  side.  (G. 
669.) 

A  Magnet  will  polarize  a  Bar  of  Iron.  —  If  a   bar 

of  iron  n  s,  and  a  magnet  N  S  (Fig.  145),  be  placed  end  to 
end,  the  iron  itself  becomes  a  magnet.  That  it  is  a 
magnet,  may  be  shown  by  its  power  to  attract  or 
repel  the  poles  of  another  magnet.  Both  kinds  of 
magnetism  are  developed  in  it,  and  hence  we  call  it 
polarized. 

Each  pole  of  a  magnet  will  always  induce  the  op- 
posite kind  of  magnetism  in  that  end  of  the  bar 
which  is  nearest  to  it. 

Unlike  frictional  electricit3r,  there  is  no  discharge 
of  magnetism  when  opposite  kinds  are  brought  to- 
gether :  the  polarization  takes  place  even  when  the  lg*  14  ' 
bar  is  in  contact  with  the  magnet,  and,  if  the  bar  be  made  of 
steel,  the  polaritj^  remains  after  the  magnet  is  removed. 

Several  Bars  may  be  polarized.  —  A  second  bar  may  be 
placed  with  one  end  near  to  the  first,  and  it  will  be  found  to 
be  polarized  ;  so  a  third  may  be  polarized  by  the  second  :  the 
series  may  be  continued  further,  but  the  force  is  less  in  each 
successive  magnet.  To  illustrate  by  experiment :  from  the 
north  pole  of  a  strong  bar  magnet  hang  a  key ;  from  the 
lower  end  of  this  one  a  smaller  key  ma}'  be  hung ;  a  third 
still  smaller,  or  a  nail,  will  be  held  by  this^,  and  a  tack  will 
cling  to  the  lower  end  of  the  last.  The  series  of  keys  and 


244  NATURAL   PHILOSOPHY. 

nails  has  become  a  series  of  magnets,  each  with  its  north 
and   south   pole,  their  north  poles  all  directed  downward. 
(See  Fig.  146.) 
All   the   Molecules   of    a   Magnet   are  polarized.  — 

Now,  the  molecules  of  a  magnet  are  as  truly  separate  from 
each  other  as  the  several  magnets  in  the  series  just  described, 
and  it  is  thought  that  each  molecule  is  a  magnet, 
with  its  north  and  its  south  pole.  Acting  through 
the  minute  distances  that  separate  them,  each  one 
is  polarizing  its  neighbors  ;  and  hence,  like  the  series 
of  bars,  their  north  poles  must  be  all  arranged  in 
one  direction,  their  south  poles  in  the  other.  Both 
kinds  of  magnetism  act  upon  each  separate  molecule, 
and  keep  it  in  a  magnetic  state.  There  is  no  trans- 
fer of  the  force  from  one  molecule  to  another,  as 
there  is  of  electricity  in  a  charged  body,  so  there 
can  be  no  discharge  of  magnetism.  A  magnet,  like 
a  bod}~  charged  with  electricity,  may  polarize  an- 
other, but  it  can  not,  like  the  charged  body,  become 
neutral  by  giving  up  its  force. 

then,  is  the  middle  of  a  magnet  neutral, 


F-     14( 

*  while  only  toward  its  ends  do  the  forces  show  them- 

selves ?  Not  because  the  force  of  one  kind  leaves  the  mole- 
cules of  one  end  and  goes  to  the  other,  but  because  in  the 
middle  of  the  series  the  two  forces  are  equal  and  in  opposite 
directions,  and  must  neutralize  each  other. 

100.  If  a  bar  magnet  be  supported  so  as  to  move  freely  in 
a  horizontal  direction,  it  will  rest  only  when  its  poles  point 
north  and  south  or  nearly  so  ;  its  variation  is  subject  to  both 
annual  and  diurnal  changes.  (G.  679.) 

If  a  Bar  Magnet  be  supported.  —  A  magnet  may  be 
supported  in  three  ways  so  as  to  have  free  motion.  It  ma}' 
be  balanced  upon  a  pivot.  (See  Fig.  147.)  It  may  be 
hung  from  a  fixed  support  \>y  a  fine  thread  tied  about  its 
middle  point  (Fig.  148).  Or  it  may  be,  for  purposes  of 
simple  experiment,  fastened  to  a  cork,  and  laid  upon  water. 


NATURAL   PHILOSOPHY.  245 

It  will  point  North  and  South.  —  The  magnet  sup- 
ported in  either  of  the  ways  mentioned  will  swing  back  and 
forth  until  it  finally  settles  to  rest,  and  it  will  then  be  found 
pointing  north  and  south.  The  end  which  points  north  is 
called  the  NORTH  POLE  :  it  is  evident,  however,  that  its 
magnetism  is  of  the  kind  opposite  to  that  of  the  north 
magnetic  pole  of  the  earth  toward  which  it  points. 

A  slender  bar  magnet  thus  balanced  is  called  a  MAGNETIC 
NEEDLE.  Such  a  needle  is  used  by  mariners  to  direct  them 
in  their  long  voyages  across  the  ocean.  For 

this  purpose  it  is  placed         J 
over  a  card  upon  which 
the     "points     of    com- 
pass,' '     north,     south,  n     \    & 
east,  west,    and   others, 
are    marked ;    and,    for 
protection,    put    into    a 

147'  box  supported  by  pivots,      vis'  148' 

so  that  it  will  keep  the  needle  in  a  horizontal  position  amid 
all  the  rolling  or  plunging  motions  of  the  ship.  Such  an 
arrangement  is  called  the  MARINER'S  COMPASS. 

Its  Variation.  —  While  it  is  true  that  the  needle  points 
in  a  direction  which  ma}r  be  described  as  north  and  south, 
we  must  not  understand  that  this  description  is  exact.  In- 
deed, the  needle  seldom  points  exactly  north  and  south. 
There  are  places  at  which  it  does  ;  there  are  others  at  which 
it  points  east  of  north  ;  and  others  at  which  it  points  west 
of  the  true  north  and  south  line.  Its  deviation,  or,  in  other 
words,  what  it  lacks  of  pointing  in  a  true  north  and  south 
line,  is  called  its  VARIATION. 

The  Line  of  no  Variation.  —  If  those  places  on  the 
earth's  surface  at  which  the  needle  points  due  north  and 
south  be  joined  by  a  line,  this  line  is  called  the  LINE  OF  NO 
VARIATION.  This  line  goes  quite  around  the  globe  in  a  north 
and  south  direction.  It  is,  however,  an  irregular  line,  bend- 
ing now  to  the  eastward  and  then  to  the  westward.  We 


246  NATUBAL  PHILOSOPHY. 

may  trace  its  general  course  through  North  America,  by 
remembering  that  it  strikes  the  continent  near  Cape  Look- 
out, on  the  coast  of  North  Carolina,  passes  through  Staunton 
in  Virginia,  a  little  east  of  Cleveland  in  Ohio,  across  Lake 
Erie,  and  thence  onward  to  Hudson  Bay. 

At  places  east  of  this  line  the  variation  is  toward  the 
west ;  at  places  west  of  it  the  variation  is  toward  the 
east. 

The  Annual  Variation.  —  The  variation  of  the  needle 
at  any  place  is  continually  changing.  For  example :  the 
variation  at  Washington,  D.C.,  was  36'  west  in  the  year 
1800,  but  in  1860  it  had  increased  to  2°  54'.  Such  a  change 
is  going  on  }'ear  by  year  at  all  places.  The  variation  in- 
creases for  several  years,  and  then  again  diminishes.  So  the 
needle  vibrates,  first  westward,  then  eastward,  and  back 
again,  taking  man}7  years  to  make  a  single  vibration. 

The  Daily  Variation.  —  Besides  this  annual  variation, 
the  needle  has  a  daily  variation,  much  greater  in  summer 
than  in  winter  —  amounting  to  about  15'  in  the  former,  and 
only  about  10'  in  the  latter.  At  about  8  A.M.,  the^orth 
pole  begins  to  swing  westward,  and  this  motion  continues 
until  about  1  P.M.  Soon  after  this  time  it  slowly  moves 
back  toward  the  east  until,  at  about  10  P.M.,  it  has  reached 
its  starting  point.  It  then  moves  west  again  until  about 
3  A.M.,  after  which  it  swings  back  to  the  eastward  until 
8  A.M.  It  completes  these  two  full  vibrations  every  twenty- 
four  hours. 

101.  If  a  magnetic  needle  be  allowed  to  move  freely  up 
and  down,  it  will  seldom  rest  in  a  horizontal  position.  Its 
inch' nation  is  called  the  dip  of  the  needle. 

In  the  northern  hemisphere  the  north  pole  of  the  needle 
dips  ;  in  the  southern  hemisphere  the  south  pole  dips. 

The  Dip  of  the  Needle.  —  If  a  slender  steel  needle 
be  balanced  upon  a  horizontal  axis  so  that  it  may  freely 
move  up  and  down,  and  be  then  magnetized,  it  will  be  no 


NATURAL   PHILOSOPHY. 


247 


longer  balanced  :  the  north  pole  will  sink  until  the  needle 
takes  a  position  very  much  inclined  (Fig.  149).  The  amount 
of  this  inclination  is  called  the  DIP  OF  THE  NEEDLE. 

In  the  southern  hemisphere  the  needle  also  takes  an  in- 
clined   position,    but   it 
is  the    south   pole  that 
points  downward. 

As  the  dipping  needle 
is  carried  farther  north, 
the  dip  increases  until  a 
point  is  reached  where 
the  needle  stands  in  a 
vertical  position.  Of 
course  this  point  must 
be  the  north  magnetic 
pole  of  the  earth :  it  is 
a  curious  fact,  that  it  is 
not  the  same  as  the 
geographical  north  pole. 
It  is  in  latitude  70°  5' 
N.  and  longitude  96°  45' 
W.,  — a  little  north  and 
west  of  Hudson  Ba 
year  1832. 

Then,  traveling  southward  in  the  southern  hemisphere, 
the  south  pole  of  the  needle  dips  more  and  more,  and  there 
is  evidently  a  south  magnetic  pole  of  the  earth.  This  point 
has  never  yet  been  found. 


Fig.  149. 

It  was  found  by  Capt.  Ross,  in  the 


X  SECTION    III. 
ON  DYNAMICAL   ELECTRICITY. 

102.  A  current  of  electricity  may  be  obtained  by  chemical 
action  in  a  simple  voltaic  cell,  or  better  in  a  Grove,  a 
Bunsen,  or  other  form  of  battery.  (G.  772-774,  783.) 


248 


NATURAL   PHILOSOPHY. 


Different  Names  used.  —  Frictional  electricity  shows 
itself  by  a  single  discharge,  or,  in  the  case  of  the  sparks  of 
a  Holtz  machine,  in  a  series  of  discharges  which  follow  at 
intervals ;  but  in  DYNAMIC  electricity  there  is  a  continuous 
action  like  the  steady  flow  of  a  stream,  and  hence  it  is  ver}* 
properly  called  CURRENT  electricit}*.  Because  it  was  discov- 
ered by  Galvani  it  has  been  called  GALVANIC  electricity  ;  and, 
because  of  Volta's  valuable  researches,  it  is  also  known  as 
VOLTAIC  electricity. 

Chemical  Action.  —  Put  some  bits  of  common  zinc  into 
a  goblet,  and  pour  upon  them  some  weak  sulphuric  acid. 
The  fluid  \fdll  soon  begin  to  boil  violently,  and  bubbles  of 
Ivydrogen  gas  will  be  given  off,  so  that  often,  if  a  lighted 
match  is  held  near,  the  gas  will  take  fire.  This  will  give  the 
curious  appearance  of  water  on  fire.  After  a  while  the  action 
will  stop,  but  not  until  much  and  perhaps  all  the  zinc  has 
been  used  up. 

In  this  case  both  the  zinc  and  the  acid  are  changed  into 
other  substances,  and  on  this  account  the  action  is  called  a 
CHEMICAL  ACTION. 

None  with  Pure  Zinc.  —  Common  zinc  is  impure,  and 
if  the  pure  metal  be  used  for  the  ex- 
periment almost  no  chemical  action 
will  occur.  Or  let  the  zinc  be  amal- 
gamated, that  is,  covered  with  a  coat- 
ing of  mercury,  and  there  will  be  very 
little  chemical  action. 

No  bubbles  of  gas  form  where  cop- 
per is  used  instead  of  zinc. 

The  Simple  Cell.  —  The  simple 
cell  is  represented  in  Fig.  150.  Into 
a  glass  vessel  is  put  a  quantity  of 
water,  mixed  with  a  little  sulphuric 
acid.  A  strip  of  copper  and  another 
of  amalgamated  zinc  are  inserted  in 
this  liquid,  and  from  the  upper  ends  of  these  strips  two  metal- 


NATURAL  PHILOSOPHY.  249 

lie  wires  project.  Now,  when  these  two  wires  are  brought 
together,  a  multitude  of  little  bubbles  of  gas  rising  alongside 
of  the  copper  strip  show  that  there  is  chemical  action ;  and, 
if  the  ends  of  the  wires  be  brought  together  and  then  carefully 
separated  in  the  dark,  a  very  delicate  spark  may  be  seen 
between  them,  showing  that  electricity  is  produced. 

The  Chemical  Action.  —  The  zinc  takes  the  place  of 
Irydrogen  in  the  acid,  and  forms  zinc  sulphate.  This  re- 
mains dissolved  in  the  fluid  while  the  hydrogen  is  forced 
along  from  molecule  to  molecule  through  the  acid  until  it 
reaches  the  copper  plate  where  it  escapes  in  bubbles.  This 
chemical  action  is  believed  to  be  the  chief  source  of  the 
electricity  in  the  circuit. 

The  electric  Conditions  in  the  Cell.  —  The  zinc  in.  the 
acid  is  positive,  the  copper  negative.  In  other  words,  the 
surface  of  the  zinc  has  a  high  potential,  the  surface  of 
the  copper  a  low  potential,  and  hence  electricity  passes  from 
zinc  through  the  liquid  to  copper  to  restore  the  equilibrium. 
But  the  chemical  action  again  quickly  renews  the  difference 
of  potential,  and  another  discharge  follows.  A  very  rapid 
charge  and  discharge  throughout  the  circuit  —  so  rapid  as 
to  seem  continuous  —  is  what  is  called  the  ELECTRIC  CUR- 
RENT. 

The  Direction  of  the  Current. — From  the  -f-  or  gen- 
erating plate  (which  is  always  the  metal  acted  upon  by  the 
fluid)  the  +  electricity  passes  through  the  liquid  to  the  — 
plate,  then  through  the  wires  back  to  the  -f-  plate. 

The  Poles.  —  The  ends  of  the  two  wires  are  called  the 
POLES  or  the  ELECTRODES  of  the  circuit :  that  from  the  cop- 
per strip  is  the  positive  pole ;  the  one  from  the  zinc  strip  is 
the  negative  pole. 

Enfeeblement  of  the  Current.  —  The  current  in  this 
simple  cell  rapidly  grows  weaker.  There  are  three  principal 
reasons  for  this  ;  viz.  :  — 

First,  The  acid  is  being  neutralized  by  the  zinc.  The 
chemical  action  diminishes  on  this  account.  This  difficulty 


250  NATURAL  PHILOSOPHY. 

can  only  be  remedied  by  renewing  the  acid  from  time  to 
time. 

Second,  There  is  local  action,  that  is,  an  action  between 
the  impurities  and  the  particles  of  the  generating  plate,  by 
which  a  multitude  of  little  circuits  are  made,  so  that  the 
energy  of  the  plate  is  not  thrown  into  the  general  current. 

This  difficulty  can  be  remedied  by  amalgamating  the  zinc, 
which  is  done  by  immersing  the  clean  zinc  in  mercury. 
No  chemical  action  then  occurs  until  the  wires  are  brought 
together,  or  the  circuit  is  closed. 

Third,  There  is  the  "  polarization  "  of  the  negative  plate. 
A  layer  of  hydrogen  gradually  fixes  itself  upon  the  surface 
of  the  copper,  and  we  have  a  surface  of  Irydrogen  instead 
of  copper.  The  plate,  in  this  way,  gradually  becomes  + 
instead  of  — ,  and  the  difference  of  potential  disappears. 

This  difficulty  can  be  remedied  only  by  managing  to  use 
up  the  hydrogen  in  some  way,  so  that  it  shall  not  come  in 
contact  with  the  —  plate.  This  may  be  accomph'shed  by 
using  a  second  fluid. 

In  Grove's  Cell.  —  In  Grove's  cell  two  metals,  zinc  and 
platinum,  and  two  liquids,  dilute  sulphuric  acid 
and  nitric  acid,  are  used.  The  peculiar  mode 
of  putting  these  together  may  be  understood 
by  an  attentive  stud}T  of  Fig.  151. 

A  glass  vessel,  V,  is  partly  filled  with  dilute 
sulphuric  acid.  Into  this  fluid  is  placed  a 
zinc  cylinder,  Z,  with  a  slit  from  top  to  bot- 
151.  tom^  to  auow  foe  fluid  to  circulate,  both  inside 
and  outside  of  it,  freely.  Inside  of  the  zinc  cylinder  is  put 
a  porous  earthenware  cup.  Into  this  cup  is  poured  strong 
nitric  acid,  and  a  strip  of  platinum  is  inserted  in  this  fluid. 
One  wire  is  fastened  to  the  zinc,  and  another  to  the  platinum. 
These  may  be  brought  together  to  close  the  circuit. 

The  platinum  pole  is  positive;  the  zinc  pole  is  negative. 
What  becomes  of  the  Hydrogen  ?  —  There  is  the  same 
chemical  action  as  in  the  zinc-copper  or  simple  cell,  but  the 


NATURAL   PHILOSOPHY. 


251 


hydrogen,  on  its  way  to  the  platinum,  must  enter  the  nitric 
acid.  The  nitric  acid  is  decomposed  by  the  hydrogen  which 
takes  oxygen  from  it,  and  the  two  remain  in  the  harmless 
form  of  water. 

Bunsen's  Cell.  —  Bunsen's  cell  (Fig.    152)   differs  from 
the  one  just  described,  by  having  a  carbon  cylinder,  or  rod, 


Fig.  152. 

fn  place  of  the  strip  of  platinum.  This  does  not  greatly 
diminish  its  action,  while  it  makes  it  much  cheaper,  plati- 
num being  a  very  costly  metal. 

Other  Forms.  —  There  are  man}"  varieties  of  voltaic  cell 
in  market.  They  are  made  by  ingeniously  varying  the 
materials  and  shape  to  fulfil  the  condition  for  a  current. 

This  is  the  Condition. — There  shall  be  two  metals  and 
a  liquid  so  related  that  the  liquid  shall  act  chemically  upon 
one  more  than  upon  the  other. 


252  NATURAL   PHILOSOPHY. 

103.  Ohm's   law  states  that  the  strength  of  the  current 
is  equal  to  the  electro-motive  force  divided  by  the  resistance. 

Definitions.  —  "The  force  by  which  electricity  is  set  in 
motion  in  the  circuit  is  called  the  ELECTRO-MOTIVE  FORCE." 
It  is  commonly  regarded  as  the  difference  of  potentials  main- 
tained by  the  cell. 

"  The  quantity  of  electricity  which,  in  a  unit  of  time, 
flows  through  a  section  of  the  circuit,  is  called  the  STRENGTH 
OF  CURRENT."  It  is  also  called  INTENSITY. 

No  substance  is  a  perfect  conductor  of  electricity,  and 
some  substances  forbid  its  passage  altogether.  This  opposi- 
tion to  the  passage  of  the  current  is  called  RESISTANCE. 

The  resistance  which  a  wire  offers  to  the  action  of  elec- 
tricity through  it  depends  upon  the  material  of  which  it  is 
made,  and  upon  its  size.  The  metals  are  the  best  con- 
ductors, silver  standing  at  the  head  of  the  list,  copper  next, 
and  lead  being  among  the  poorest.  The  larger  and  the 
shorter  the  wire,  the  less  resistance  it  offers. 

The  Formula.  —  The  relation  of  these  values  as  stated 

above  in  Ohm's  law  may  be  simply  expressed  in  the  formula, 
-p 

(7=  -^;  in  which  C  stands  for  strength  of  current,  E  for  the 
H 

electro-motive  force,  and  R  for  the  resistance. 

104.  The   resistance   in   a   circuit   is   partly  in  the   cell, 
internal,  and  partly  in  the  conductors  outside,  external. 

The  best  effect  is  obtained  in  the  use  of  a  battery  when 
the  internal  and  external  resistances  are  equal. 

If  the  resistance  to  be  overcome  is  small,  we  need  a 
battery  of  low  resistance ;  but,  if  it  is  great,  a  battery  of 
high  resistance. 

A  Battery  of  Low  Resistance.  —  The  resistance  in  the 
cell  depends  chiefly  on  the  fluid,  because  the  Conductivity 
of  the  metals  is  so  vastly  greater  than  that  of  the  fluid. 

Now,  we  have  seen  that  the  resistance  of  a   conductor 


NATURAL   PHILOSOPHY.  253 

depends  on  the  area  of  its  cross  section.  If  we  enlarge  the 
plates  in  the  cell  we  make  the  area  of  the  conducting  liquid 
between  them  larger,  and  so  diminish  its  resistance. 

This  is  most  conveniently  done  by  taking  several  common 
cells,  and  joining  all  their  zincs  together  by  a  wire  outside, 
and  all  their  coppers  by  another  wire.  This  forms  a  battery 
of  low  resistance.  It  is  sometimes  called  a  battery  for 
quantity. 

Its  Electro-Motive  Force.  —  In  the  zincs,  all  joined 
together,  there  is  the  same  potential  as  if  there  were  only 
one  alone.  There  is  no  greater  difference  of  potential  in 
zincs  and  coppers  than  if  there  were  a  single  cell ;  that  is, 
the  electro-motive  force  is  not  increased. 

Its  Strength  of  Current.  —  By  linking  cells  in  this  way, 
the  internal  resistance  is  diminished,  while  the  electro-motive 
force  remains  the  same.  If  there  were  no  external  resistance, 

E 

then  R  in  the  formula  G  =  -=  would  be  less  and  less  as  the 

H 

TF 

number  of  cells  increases,  and  hence  -=  would  be  greater ; 

that  is,  the  strength  of  current,  C,  would  be  greater  in  pro- 
portion to  the  number  of  cells. 

Hence,  when  in  using  electricity,  there  is  little  external 
resistance,  a  loio-resistance  battery  should  be  used. 

A  Battery  of  High  Resistance.  —  We  may  link  the 
cells  together  in  another  way.  Let  the  zinc  of  one  be  joined 
to  the  copper  of  the  next,  and  its  zinc  with  the  copper  of  the 
next  throughout  the  series,  and  finally  close  the  circuit  by 
joining  the  first  copper  with  the  last  zinc. 

This  forms  a  battery  of  high  resistance.  It  is  sometimes 
called  a  batteiy  for  intensity. 

Its  Electro-Motive  Force.  —  In  this  case  each  zinc  acts 
separately,  and  the  electro-motive  force  of  the  battery  is  the 
sum  of  the  electro-motive  forces  of  the  separate  cells.  For 
n  cells  of  the  same  kind  it  would  be  n  E. 

The  Resistance,  —  The   internal   resistance   is   also   in- 


254  NATUKAL    PHILOSOPHY. 

creased  in  the  same  ratio,  for  a  dozen  cells  yield  a  dozen 
times  as  much  resistance  as  one  cell.  But  the  external  re- 
sistance is  not  at  all  affected  by  changing  the  number  of 
cells ;  and  if  we  suppose  it  to  be  very,  very  much  greater 
than  the  internal  resistance  of  one  cell,  it  would  also  be  much 
greater  than  the  resistance  of  a  dozen  cells,  and  the  total  resist- 
ance may  be  very  little  greater  with  n  cells  than  with  one. 

The  Strength  of  Current.  —  Then  in  the  formula  C  =  -. 

R' 

with  n  cells  the  numerator  is  increased  to  n  E.  while  the 
denominator  remains  almost  unchanged.  Hence  C  is  in- 
creased almost  n  times.  That  is :  The  strength  of  current 
increases  almost  in  proportion  to  the  number  of  cells. 

Hence,  when  in  using  electricity,  there  is  great  external 
resistance,  a  high-resistance  batter}*  should  be  used. 

Quantity  and  Intensity.  —  Large  surfaces  of  elements 
in  the  battery  yield  large  quantities  of  electricity :  a  large 
number  of  cells  in  series  yields  electricity  of  great  intensity. 

The  greatest  difference  between  current  electricity  and 
frictional  electricity  is  this  :  current  electricity  is  remarkable 
for  its  great  quantity  but  feeble  intensity,  while  frictional 
electricity  is  equally  remarkable  for  its  great  intensity  but 
small  quantity. 

105.  Current  electricity  produces  :  — 

Heat  whenever  it  is  resisted  in  its  action. 

Light  whenever  its  intensity  enables  it  to  leap  through  air, 
or  to  render  a  poor  conductor  incandescent. 

Magnetism  whenever  its  conductor  encircles  a  bar  of 
iron. 

Chemical  action  whenever  it  goes  through  an  electrolyte. 
(G.  809-813,  816-820,  854,  856.) 

Heat.  —  Electricity,  when  resisted  in  ixs  action,  shows 
itself  as  heat.  When  it  acts  through  a  fine  wire,  the  wire 
may  be  made  red-hot,  and  in  man}'  cases  melted,  by  the 
Jieat  produced.  Several  inches  of  fine  iron  wire  may  be  thus 


NATURAL   PHILOSOPH  t.  255 

melted  by  a  batteiy  of  twelve  or  fifteen  cells.  This  power 
of  electricit}7  is  applied  to  the  exploding  of  gunpowder,  for 
blasting  rocks.  For  this  purpose,  a  cartridge  is  made  by 
filling  a  tin  tube  with  gunpowder,  and  corking  its  ends 
tightly.  Through  one  of  the  corks  two  copper  wires  pass, 
joined  in  the  powder  by  a  fine  steel  wire  soldered  to  their 
ends.  The  copper  wires  are  then  connected  with  the  poles 
of  a  distant  battery.  The  instant  that  the  circuit  is  made, 
the  fine  wire  in  the  gunpowder  becomes  intensely  hot,  and 
its  heat  explodes  the  gunpowder. 

Light.  —  When  the  wires  which  lead  from  the  poles  of  a 
powerful  battery  are  tipped  with  charcoal  points,  if  these 
points  are  brought  in  contact  and  then  separated  for  a  short 
distance,  the  space  between  them  will  be  bridged  over  by  an 
arc  of  blinding  light.  On  examination,  this  light  is  found 
to  be  due  to  the  intense  whiteness  of  the  carbon  tips,  chiefly, 
but  not  to  their  combustion,  since  in  a  vacuum,  where  com- 
bustion can  not  occur,  the  light  is  of  equal  intensit}'. 

The  heat  of  this  arc  of  light  is  wonderfully  intense. 
Platinum,  more  difficult  to  melt  than  other  metals,  melts  in 
this  heat  like  wax  in  the  flame  of  a  taper.  Even  quartz, 
and  other  bodies  equally  difficult  to  melt,  are  fused  by  it 
readily. 

The  electric  light  is  produced  not  only  by  the  "electric 
arc,"  but  also  by  "incandescence."  If  a  platinum  wire, 
or  a  small  rod  of  carbon,  is  placed  in  the  circuit  of  a  battery 
of  high  resistance,  it  will  be  heated  intensely,  and  glow  with 
a  fine  white  light. 

Electric  lamps  arc  of  these  two  classes :  some  are  con- 
structed to  yield  the  light  by  the  arc,  others  to  3*ield  it  by 
incandescence. 

Mag-iietism.  —  Bars  of  soft  iron  inclosed  in  coils  of  wire 
are  called  ELECTRO-MAGNETS.  The  coil  is  generally  called 
a  HELIX.  If  the  two  ends  of  the  coil  be  fastened  to  the 
poles  of  a  battery,  the  electricity  darts  instantly  through  the 
coil,  ancl  the  iron  becomes  a  magnet.  The  bar  of  iron  may 


256 


NATURAL   PHILOSOPHY. 


be  of  an}'  form ;  when  in  the  shape  of  the  horseshoe  mag- 
net, the  coil  is  made  in  two  parts,  one  encircling  each  arm 
of  the  iron.  A  horseshoe  electro-magnet,  A  B,  is  seen  in 
Fig.  153. 

The  strength  of  electro-magnets  is  something  surprising. 
One  belonging  to  Yale  College,  weighing  59  pounds,  lifted  a 
weight  of  2,500  pounds.  This  wonderful  power  is  developed 

only  when  an  armature,  c 
d  (Fig.  153),  is  in  contact 
with  the  poles.  Without 
this,  the  magnet  will  not 
lift  a  tenth  part  of  what  it 
could  otherwise  sustain. 

The  iron  is  magnetic  only 
while  the  electricity  acts 
around  it.  Let  the  circuit 
be  in  an}'  wa}"  broken,  and 
the  grasp  of  the  giant  is  at 
once  loosed  ;  the  load  falls. 
On  again  making  the  cir- 
cuit, the  magnet  is  instantly 
as  strong  as  before.  The 
rapidity  with  which  an  iron 
bar  will  thus  receive  and 
part  with  its  magnetism,  as 
the  circuit  is  made  and 
broken,  is  truly  astonishing. 
B}-  the  electric  register  for 

vibrations,  the  author  has  caused  an  electro-magnet  to  un- 
dergo this  change  at  the  rate  of  8,400  times  a  minute.    Yx' 
The  Electric  Telegraph  acts  on  this  Principle.  —  It 
is   upon   this  principle   that  the  electric  telegraph  has  ena- 
bled man  to  send  his  thoughts,  with  lightning-speed,  across 
continents  and   under  oceans,  to   his   most   distant   fellow- 
men. 
Having  found  that  a  bar  of  iron  will  become  magnetic  as 


NATURAL   PHILOSOPHY.  257 

often  as  electricity  is  sent  round  it,  and  cease  to  be  so  on 
the  instant  the  circuit  is  opened,  let  us  next  notice  that 
the  wires  conveying  the  force  may  be  of  any  length,  even 
miles,  and  hence  the  battery  may  be  in  one  city,  while  the 
magnet  may  be  in  another,  and  still  an  armature  will  be 
drawn  against  its  poles  ever}*  time  the  circuit  is  made.  Now, 
if  the  motion  of  an  armature  to  and  from  the  poles  can  be 
made  to  write,  then  can  messages  be  sent  from  one  city  to 
another. 

The  apparatus  consists  of  three  parts :  the  key,  the  line, 
and  the  register. 

The  Key  is  an  instrument  by  which  the  circuit  can  be 
made  and  broken  at  will.  It  is  in  the  office  from  which  the 
message  is  to  be  sent.  A  brass  lever,  L  (Fig.  154),  moves 
on  an  axis,  A.  Two  projections,  n  and  m,  from  its  lower 
side,  are  just  above  two 
others,  one  of  which,  a,  is 
joined  by  a  wire  with  the 
battery,  while  from  the 
axis,  A,  another  wire 
reaches  to  the  distant  sta- 
tion. By  pressing  the  fin- 
ger on  the  end  of  this  lever,  the  point  is  brought  in  contact 
with  the  battery- wire  at  a,  and  the  electricity  can  then  act 
through  the  lever,  from  the  battery-wire  to  the  wire  from  the 
axis.  Let  the  finger  be  lifted,  and  the  lever  will  rise  by  the 
action  of  a  spring,  s,  and  the  circuit  is  broken. 

The  Line  consists  of  a  wire,  L,  reaching  from  the  key 
over  the  country  to  distant  places.  At  first  two  wires  were 
used,  one  from  the  positive  pole,  the  other  from  the  nega- 
tive pole,  of  the  battery ;  but  it  was  soon  found  that  the 
earth  may  take  the  place  of  one  of  these  wires. 

The  Register  is  shown  in  Fig.  155.  One  of  the  screw- 
cups  at  the  end  of  the  instrument  is  connected  with  the  line 
wire,  L,  which  reaches  from  the  key  of  the  distant  station, 
while  the  other,  M,  is  connected  with  the  earth.  When  tho 


258 


NATURAL   PHILOSOPHY. 


circuit  is  made,  the  electric  force  darts  around  the  electro- 
magnet, and  draws  the  armature  down  against  its  poles  :  this 
raises  the  long  arm  of  the  lever,  and  presses  the  steel  point, 
I,  against  a  strip  of  paper,  which  is  pulled  along  from  the 
spool,  E,  by  clock-work.  When  the  circuit  is  broken,  the 
armature  is  released  from  the  poles  of  the  electro-magnet ; 
the  long  arm  of  the  lever  falls  by  its  own  weight,  or  by  the 
force  of  a  spring,  and  the  point  is  removed  from  the  paper. 
If  the  point  press  the  paper  for  an  instant  only,  a  dot  will 


Fig.  155. 

be  made,  but,  if  it  be  held  against  it  for  a  longer  time,  a  dash 
will  be  left  upon  it.  Now,  the  letters  of  the  alphabet  are 
represented  by  dots  and  dashes.  Two  operators  who  know 
this  alphabet  can  communicate  with  each  other ;  one  by 
pressing  the  key  causes  a  series  of  dots  and  dashes  to  be 
marked  upon  the  paper  of  the  register  at  a  distant  place, 
while  the  other  can  read  this  written  language.  A  skillful 
operator  knows  the  letters  by  the  sound  of  the  clicks  of  the 
instrument.  He  uses  a  "  sounder  "  instead  of  a  writer. 
Such  is  an  outline  of  the  essential  parts  of  the  electric 


NATURAL  PHILOSOPHY. 


259 


telegraph.  A  larger  work,  or,  better,  a  visit  to  the  tele- 
graph-office, will  make  one  full}-  acquainted  with  the  many 
details  of  its  operation. 

The  steam-engine  and  the  electric  telegraph  may  be  re- 
garded as  the  body  and  the  spirit  of  modern  civilization,  the 
first  distributing  matter,  the  second  thought;  both  laboring 
toward  a  more  general  diffusion  of  comfort  and  knowledge 
and  s}rmpathy  among  men. 

Chemical  Action.  —  Acidulated  water  will  be  decomposed 
by  the  current  when  the  electrodes  of  a  battery  of  two  or 
mdre  cells  in  series  are  immersed  in  it. 

The  electrodes  of  the  battery  (Fig.  156)  pass  up  through 
the  bottom  of  a  vase  into  the  very  dilute  acid,  and  two  tubes 


filled  with  the  liquid  are  inverted  over  them.  The  moment 
the  circuit  is  closed,  a  multitude  of  gas-bubbles  break  from 
the  electrodes,  and  are  caught  in  the  tubes  above.  These 
gases  prove  to  be  hydrogen  and  oxygen,  —  the  constituents 
of  water. 

Various  other  liquids  may  be  decomposed  by  the  current ; 
all  such  are  called  ELECTROLYTES. 


260 


NATURAL   PHILOSOPHY. 


Fig.  157. 


106.  The  current  swaj's  a  magnetic  needle  near  which  it 
flows. 

The  galvanometer  detects  and  measures  the  current  on 
this  principle. 

Effect  on  the  Needle.  —  Let  a  magnetic  needle  be  placed 
in  a  rectangle  of  wire  provided  with  pole-cups  as  shown  in 
Fig.  157.  It  will  be  found  that  whenever  the  current  flows 
through  the  wire,  the  needle  will  turn. 
The  current  tends  to  put  the  needle  at 
right  angles  to  its  own  direction. 

If  the   current  pass  from  south  to 
north,  above  the  needle,  the  north  pole 
will  turn  to  the  west;  if  from  north  to 
south,  the  north  pole  will  turn  to  the 
east.     If  the  current  pass  below  the 
needle,  the  north  pole  turns  in  direc- 
tions opposite  those  just  mentioned. 
The  motion  of  the  needle  declares  the  presence  of  a  cur- 
rent ;   the  direction  of  the  motion  tells  the  direction  of  the 
current ;  and  the  distance  the  pole  moves  measures  the  strength 
of  the  current. 

The  Astatic  Needle.  —  This  consists  of  two  needles 
fastened  together  with  the  north  pole  of  one  opposite  the 
south  pole  of  the  other.  The  ends 
of  this  needle  are  equally  attracted 
and  repelled  by  the  earth's  magnet- 
ism. But  the  north  pole  is  usually 
left  a  little  stronger  than  its  com 
panion,  so  that  the  earth's  magnet- 
ism is  not  quite  neutralized,  and 
the  needle  will  be  ' '  true  to  the 
pole,"  although  with  a  ver}T  feeble 
force. 

The  Galvanometer.  —  A   sen- 
sitive form  of  this  instrument  is  shown  in  Fig.  158. 


Fig.  158. 


NATURAL   PHILOSOPHY. 

The  astatic  galvanometer  consists  of  a  coil  of  very  fine 
silk-covered  copper  wire  wound  on  a  flat  wooden  bobbin ; 
an  astatic  needle,  the  upper  half  near  the  upper  plane-sur- 
face of  the  helix,  the  under  one  in  the  middle  section  of  the 
helix ;  the  needle  is  suspended  by  a  silk  fiber ;  a  graduated 
circle  is  placed  under  the  upper  needle  ;  the  coil  rests  on  a 
mahogany  base  with  leveling  screws,  and  is  covered  by  a 
glass  shade.  (Ritchie.) 

107.  Induced  or  secondary  currents  are  developed  in  a 
conductor :  — 

1st,  B}-  the  approach  or  departure  of  a  batter}7  current. 

This  principle  is  embodied  in  the  Ruhmkorff  coil. 

2d,  By  the  approach  or  departure  of  a  magnet. 

This  principle  is  embodied  in  magneto-electric  machines 
and  the  telephone.  (G.  874-876,  883,  886,  889.) 

I.  —  INDUCTION    BY  A   CURRENT. 

Description  of  Apparatus.  —  Two  coils,  one  containing 
a  few  feet  of  stout  copper  wire,  and  called  the  primary  coil, 
and  another  containing  a  very  great  length  of  fine  copper 
wire,  and  called  the  secondary  coil,  are  so  made  that  the 
primaiy  may  be  placed  inside  the  secondary  or  taken  out  at 
pleasure  (Fig.  159).  The  primary  is  connected  with  a 
battery,  and  the  secondary  with  a  galvanometer. 

Results  of  Experiment.  —  While  the  primary  is  passing 
into  the  secondary  coil,  the  galvanometer  needle  swings,  show- 
ing a  current  in  the  secondary  moving  in  a  direction  opposite 
to  that  of  the  battery  current.  It  is  called  an  inverse  cur- 
rent. 

While  the  primary  is  being  withdrawn,  the  needle  swings 
the  other  way,  showing  a  current  in  the  secondary  coil 
moving  in  the  same  direction  as  the  battery  current.  It  is  a 
direct  current. 

But  the  current  may  be  introduced  into  the  secondary  coil, 
and  withdrawn  in  another  way.  We  may  leave  the  primary 


232 


NATURAL   PHILOSOPHY. 


coil  inside  the  secondary,  and  then  simply  close  and  open  the 
battery  circuit.  On  closing  the  circuit  the  current  darts 
through  the  primary  coil,  and  on  opening  it  the  current 
ceases.  Now  we  find  that  on  dosing  the  primary  circuit,  the 
motion  of  the  galvanometer  declares  an  inverse  current  in 
the  secondary  coil.  On  opening  the  primary  circuit,  the 
motion  of  the  galvanometer  shows  a  direct  current  in  the 
secondary  coil. 


Fig.  159. 

Induction  Coils.  —  It  is  upon  this  principle  of  induction 
that  the  Ruhmkorff  coils  are  constructed.  In  these  impor- 
tant instruments  there  is  first  a  primary  coil  of  large  copper 
wire,  inside  of  which  is  put  a  bundle  of  iron  wires.  Outside 
of  this  is  placed  the  secondary  coil,  which  is  made  of  fine 
copper  wire  many  thousands  of  feet  in  length.  The  two 
coils  are  insulated  from  each  other  with  the  utmost  care. 
The  ends  of  the  primary  coil  are  attached  to  the  battery, 
while  from  the  ends  of  the  secondary  coil  the  electricity  is 
taken  in  experiments. 

Ritchie's  Induction  Coil.  —  The  induction  coil,  as  con- 
structed by  Ritchie,  is  represented  in  Fig.  160.  The  primary 
consists  of  about  200  feet  of  stout  copper  wire.  The  sec- 


NATURAL   PHILOSOPHY.  263 

onclary  contains  about  68,000  feet  of  fine  copper  wire.  The 
two  are  separated  by  a  thick  glass  bell  whose  knob  is  seen 
at  the  top.  The  primary  circuit  is  opened  and  closed  by  a 
toothed  wheel,  b.  The  ends  of  the  secondary  are  fastened  to 
sliding  rods  on  glass 
supports.  When  the 
poles  of  a  battery  are 
placed  in  the  bind- 
ing-posts s  and  c,  let 
the  circuit  be  opened 
and  closed  by  turn- 
ing  the  toothed 
wheel  6,  and  electric 
sparks  in  rapid  suc- 
cession will  leap 
through  the  air  be- 
tween the  ends  of 
the  insulated  rods. 

The    length    of    the  ~~Fig7i0o. 

spark  depends  upon 

the  size  and  insulation  of  the  coils,  and  the  strength  of  the 
6atteiy.  The  instrument  just  described  is  able  to  yield  a 
spark  nine  inches  in  length. 

II.  ^-INDUCTION   BY   A   MAGNET. 

Results  of  Experiment.  —  It  is  found  that  if  a  magnet 
be  used  instead  of  the  primary  coil  in  Fig.  159,  the  same 
effects  are  produced. 

Hence  the  motion  of  a  magnetic  pole  induces  a  secondary 
current,  in  one  direction  as  it  enters,  in  the  other  as  it 
emerges. 

If  a  bar  of  soft  iron  be  placed  in  the  secondarj^,  and  then 
a  pole  of  a  magnet  be  moved  toward  and  from  it  (Fig.  1G1), 
the  same  effects  will  be  produced.  The  soft  iron  becomes  a 
magnet  by  the  approach  of  the  pole,  and  loses  its  magnetism 
when  the  pole  departs.  This  is,  in  effect,  onh'  another  way 
to  introduce  and  withdra-w  the  magnet. 


264 


NATURAL   PHILOSOPHY. 


Finally,  insert  a  permanent  magnet  in  the  secondan*  coil, 
and  move  a  bar  or  disk  of  soft  iron  toward  and  from  its 
pole  :  currents  in  the  coil  are  induced  by  this  motion. 

The  soft  iron  becomes  magnetic  by  induction,  and  then 
affects  the  magnet  in  the  coil,  strengthening  it  b}*  approach 
and  weakening  it  by  departure. 

Hence  an}*  change  in  the  strength  of  a  magnet  will  induce 
an  electric  current  in  a  coil  which  surrounds  it. 


Fig.  161. 

Magneto-Electricity.  —  Electricity  induced  by  a  magnet 
is  called  MAGNETO-ELECTRICITY.  Man}'  forms  of  apparatus 
have  been  devised  with  which  to  generate  magneto-electricity, 
and  the  currents  of  enormous  power,  needed  for  electric 
lighting  and  other  applications  of  electricity  in  the  arts  and 
industries,  are  produced  b}'  late  and  powerful  forms  of  these 
"  dynamo-electric  machines." 

A  Simple  Form In  this  instrument  (Fig.  162),  two 

coils  of  wire,  W,  inclose  the  two  arms  of  a  bar  of  soft  iron, 
having  the  form  of  a  horseshoe  magnet,  which  by  a  band  and 
wheel,  M,  can  be  put  in  rapid  motion  in  front  of  a  venr  pow- 
erful compound  magnet,  S.  The  soft  iron  becorrtes  magnetic 


NATURAL   PHILOSOPHY. 


265 


whenever  its  ends  are  in  front  of  the  poles  of  the  permanent 
magnet,  and  hence  its  two  branches  are  being  alternately 
magnetized  in  opposite  states  at  every  turn.  The  effect  of 


Fig.  162. 

this  is  to  produce  two  opposite  currents  in  the  coils  at 
every  revolution.  These  currents  are  taken  by  the  wires, 
e,  and  thence  under  the  instrument  to  the  screw-cups,  K 
and  P.-'//^ 

The  Telephone.  —  Any  instrument  for  transmitting  sound 
to  a  distance  is  a  TELEPHONE.  Two  general  classes  of  the 
instrument  are  in  use,  —  magneto  telephones,  in  which  a  mag- 
net is  used,  and  electro-chemical  telephones,  in  which  a  bat- 
tery is  employed. 

The  Bell  Telephone.  —  The  Bell  telephone  belongs  to 
the  first  class.  Fig.  163  shows  the  inside  structure,  and  Fig. 
164  the  external  appearance,  of  the  instrument. 

B  is  a  magnet,  and  A  a  coil  of  wire  around  one  of  its 
poles.  C  is  a  thin  disk  of  sheet-iron,  called  the  diaphragm, 
very  near  but  not  touching  the  pole  of  the  magnet.  F  F  are 
wires  leading  from  the  coil  to  the  end  of  the  handle,  where 
one  is  joined  to  the  line  and  the  other  to  the  earth.  At  the 
other  end  of  the  line  is  a  second  instrument  of  just  the  same 
kind. 

Its  Action.  —  A  speaker  puts  his  lips  to  the  mouth  of  the 


266 


NATURAL   PHILOSOPHY. 


cone  of  one  instrument,  and  speaks,  while  a  listener  puts  his 
ear  to  the  mouth  of  the  other,  and  hears  what  is  spoken. 

The  air-waves  of  the  voice  vibrate  the  diaphragm  C.  Its 
motions  toward  and  from  the  pole  of  the  magnet  strengthen 
and  weaken  the  magnetism,  and  thus  send  electric  pulses 
through  the  wire  to  the  distant  station. 

The  electric  pulses  from  the  transmitting  telephone  act 
through  the  coil  of  the  receiving  telephone  at  the  other  end 
of  the  line,  and  alternately  strengthen  and  weaken  its  mag- 
net. The  diaphragm  in  front  of  this  magnet  is  attracted  by 


Fig.  163. 

it,  and,  as  the  strength  of  the  magnet  varies,  the  thin  disk 
springs  back  and  forth.  This  vibration  of  the  disk  produces 
air-waves  which  enter  the  ear  of  the  listener. 

Now,  two  sets  of  air-waves  which  are  exactly  alike  will 
affect  the  ear  in  exacth'  the  same  way,  no  matter  how  they 
are  produced,  and  hence,  all  that  is  needed  to  make  any  thing 
speak  is  to  cause  it  to  move  so  as  to  produce  just  such  air- 
waves as  the  voice  makes.  The  air- waves  of  the  voice  of 
the  speaker  vibrate  the  iron  plate  in  the  transmitter:  the 
iron  plate  in  the  receiver  vibrates  in  exactly  the  same  way, 
and  hence  the  air-waves  which  enter  the  ear  of  the  hearer 
are  faithful  copies  of  those  which  leave  the  lips  of  the 
speaker,  and  are  heard  as  the  same  sound. 


NATTJKAL  PHILOSOPHY.  267 

Hence,  by  the  telephone,  sound-waves  are  converted  into 
electric  pulses  in  the  transmitter,  and  these  electric  pulses 
reaching  the  receiver  are  converted  back  again  into  sound- 
waves. 

Edison's  Carbon  Transmitter.  —  In  the  Bell  telephone 
we  notice  that  the  transmitter  and  receiver  are  exactly  alike. 
But  an  Edison  transmitter  is  often  coupled  with  a  Bell  re- 
ceiver. The  telephone  then  becomes  electro-chemical  instead 
of  magnetic. 

The  electric  resistance  of  carbon  varies  with  the  pressure 


Fig.  164. 

upon  it,  doubtless,  because  heavier  pressure  secures  a  better 
contact  of  conductors.  This  is  the  principle  used  in  the 
Edison  transmitter. 

Pure  lampblack  is  formed  into  a  compact  button,  and 
placed  in  a  battery-circuit  which  also  includes  a  Bell  instru- 
ment at  the  distant  station.  A  diaphragm  is  fixed  so  that 
its  center  presses  gently  against  this  button.  When  the 
diaphragm  is  at  rest  a  steady  current  from  the  battery  flows 
through  the  distant  telephone.  But,  when  the  voice  of  the 
speaker  vibrates  the  diaphragm,  it  exerts  a  varying  pressure/ 
on  the  button,  and  this  varying  pressure  transforms  the 
steady  current  into  an  undulatory  one.  The  diaphragm  of 
the  receiver  is  compelled  to  vibrate  in  unison  with  these  un- 
dulations, and  emit  the  sound. 


268 


NATURAL  PHILOSOPHY. 


Fig.  165. 


The  Microphone.  —  In  the  microphone  the  transmitter 
consists  simply  of  a  rod  of  carbon,  A  (Fig.  165),  supported 
between  two  small  blocks,  C  C,  of  the  same  material,  its 

pointed  ends  resting  loosely  in 
shallow  cups  in  the  blocks.  The 
whole  is  fixed  to  an  upright  thin 
board  fastened  to  a  solid  base,  D. 
This  transmitter  is  put  into  circuit 
by  joining  one  block  to  a  battery 
by  a  wire  Y, 
and  the  other 
b}*  a  wire  X  to 
the  line  lead- 
ing to  the  dis- 
tant receiver. 
The  ticking 
of  a  watch  be- 
fore this  in- 
strument is  distinctly  heard  in  the  telephone,  and  even  the 
steps  of  a  fly  over  the  board  are  heard  by  the  distant 
listener. 

108.  Electricity  may  be  developed  by  heat:  it  is  then 
called  THERMO-ELECTRICITY.  (G.  900,  904.) 

Thermo-Electricity.  —  We  have  seen  that  electricity  will 
produce  heat ;  we  are  now  to  notice  that  heat  will  produce 
electricity.  When  two  pieces  of  different  metals  are  sol- 
dered together,  and  their  junction  heated  or  cooled,  a  current 
of  electricity  is  produced.  The  metals  antimony  and  bis- 
muth are  best  suited  to  this  purpose,  but  any  others,  or, 
indeed,  two  pieces  of  the  same  metal,  will,  in  some  degree, 
produce  the  same  effect.  Nor  is  it  quite  necessary  that 
metals  should  be  used  at  all :  other  solids,  and  even  fluids, 
give  rise  to  this  kind  of  electricity. 

Two  pieces  of  metal  soldered  together,  with  wires  at- 
tached to  their  other  ends,  through  which  the  electricity 


NATURAL   PHILOSOPHY.  269 

'  act,  is  called  a  THERMO-ELECTRIC  PAIR.  When  stronger 
currents  are  desired,  a  combination  of  pairs,  the  two  metals 
alternating  throughout,  is  used.  Such  a  combination  is  called 
a  THERMO-ELECTRIC  PILE. 

Metals  which  differ  most  in  conducting  power  and  crys- 
talline texture,  are  best  suited  to  produce  thermo-electric 
currents.  The  force  of  the  electricity  is  in  proportion  to  the 
difference  of  temperature  at  the  two  ends  of  the  pile,  pro- 
vided the  difference  does  not  exceed  80°  or  90°  F.  It  is  in 
all  cases  very  feeble;  yet  the  galvanometer  (Fig.  158) 
responds  to  so  delicate  a  current  that  the  slightest  change 
of  temperature  in  the  pile  can  be  detected  by  the  electricity 
it  produces.  Indeed,  the  thermo-electric  pile  and  galvanom- 
eter (Melloni's  apparatus),  is  the  most  delicate  thermometer 
known. 


SECTION  IV. 

REVIEW. 
I.— SUMMARY   OF  PRINCIPLES. 

The  electricity  produced  by  friction  shows  its  presence  by 
attracting  and  repelling  light  bodies. 

Two  bodies  charged  with  the  same  kind,  either  positive  or 
negative,  repel,  but,  when  charged  with  different  kinds, 
attract. 

A  charged  body  polarizes  every  other  body  in  its  neigh- 
borhood, inducing  the  same  kind  of  electricity  in  all  sides 
toward  itself,  and  the  opposite  kind  in  all  sides  away  from 
itself. 

Electricity  resides  only  upon  the  surface  of  a  charged 
body. 

Upon  the  surface  of  a  sphere,  electricity  is  uniformly  dis- 
tributed :  if  the  I  ody  is  not  a  sphere,  the  electricity  will 
be  most  intense  at  the  ends. 

The  potential   of  a  body  is  the   excess   or  defect   of  its 


270  NATURAL   PHILOSOPHY. 

electric  charge  above  or  below  that  of  the  earth  in  its 
neighborhood. 

The  electro-motive  force  is  that  which  urges  electricity 
along  over  a  conductor.  The  poorer  the  conductor,  the 
greater  the  electro-motive  force  needed  to  carry  electricity 
through  it.  In  frictional  electricity  the  electro-motive  force 
is  very  great,  as  shown  by  its  passage  through  air,  which  is 
among  the  very  poorest  conductors. 

Two  magnetic  poles  of  the  same  name  repel,  but  if  of 
different  names  the}*  attract,  each  other. 

A  pole  of  either  name  can  not  exist  alone  ;  but  both  are 
always  found  at  once  in  the  same  piece  of  metal.  The  mag- 
netic condition  is  always  a  polarized  condition.  There  is 
no  conduction  of  magnetism. 

Current  electricity  is  generated  by  chemical  action  in  a 
galvanic  cell,  which  may  consist  of  any  two  different  metals 
in  a  liquid  which  can  act  chemically  on  one  more  than  on  the 
other. 

Current  electricity  differs  from  frictional  electricity  in  its 
electro-motive  force  and  quantity.  Its  electro-motive  force 
is  vastly  less,  its  quantity  vastly  greater. 

The  +  pole  of  a  battery  is  always  that  one  which  is  con- 
nected with  the  metal  acted  on  least  by  the  liquid. 

Hydrogen  is  evolved  by  the  chemical  action,  and  clinging 
to  the  —  plate  "  polarizes  "  it.  The  current  on  this  account 
soon  becomes  weak. 

A  ' '  constant  battery  ' '  is  one  in  which  the  hydrogen  is 
prevented  from  reaching  the  —  plate  by  means,  usual!}*,  of 
a  second  liquid  which  changes  the  hydrogen  into  water. 

The  three  most  important  elements  of  a   current  are  its 

strength,  C,  its  electro-motive  force,  E,  and  its  resistance, 

pi 

R.     Ohm's  law  is  expressed  in  the  formula  C  =  —  • 

H 

Each  of  these  elements  can  be  measured  in  terms  of  ap- 
propriate units. 

The   unit  of  R  is   called    the   OHM.     A  piece  of  No.  16 


NATURAL   PHILOSOPHY.  271 

copper,  wire  (about  T^-  inch  diameter)  60  feet  long  has  a 
resistance  of  about  one  ohm.  The  resistance  of  ten  times 
this  length  of  the  same  wire  is  about  ten  ohms.  (G.  908, 
909.)  The  resistance  of  the  Atlantic  cable  is  eight  thou- 
sand ohms. 

The  unit  of  E  is  called  a  VOLT.  A  single  cell  of  Daniel's 
battery  yields  an  electro-motive  force  of  about  one  volt.  A 
Grove  or  Bunsen  cell  is  more  powerful :  its  electro-motive 
force  is  about  1.8  volts. 

The  unit  of  C  is  called  an  AMPERE.  A  current  of  one 
Ampere  strength  will  decompose  .0000945  gramme  of  water 
in  a  second. 

Electrical  measurements  are  of  the  utmost  importance  in 
telegraphy  and  in  other  practical  applications  of  electricity. 

When  great  resistance  is  to  be  overcome,  the  cells  of  a 
batter}'  should  be  joined  "  in  series."  When  the  resistance 
is  small,  the  best  effect  is  obtained  by  joining  all  plates  of  the 
same  kind  together. 

The  energy  of  the  current  may  be  converted  into  heat  or 
light  or  magnetism  or  actinism. 

Momentary  currents  are  induced  in  a  conductor  by  the 
making  and  breaking  of  a  current  in  a  conductor  near  it,  or 
by  the  approach  or  departure  of  a  magnet. 

An  undulatory  current  is  induced  in  a  conductor  by  the 
alternate  strengthening  and  weakening  of  a  primaiy  current 
near  it,  or  by  the  alternate  strengthening  and  weakening  of 
a  magnet  around  which  it  is  coiled. 

II.  —  SUMMARY   OF  TOPICS. 

89.  Electricity   by  friction. — The   electrical   machine. — 
Its  action.  —  Electroscopes.  —  Positive  and  negative.  —  The 
law.  —  Application  of  the  law. 

90.  A  charged  body. — A  non-conductor. — Potential. — 
High  and  low  potential.  — Electro-motive  force.  —  Insulated 
body.  —  Polarization.  — A  charge  b}T  polarization. 

91.  Polarization   in  series.  —  Faraday's  theory. — Differ- 


272  NATURAL  PHILOSOPHY. 

ence  between  conductors  and  non-conductors.  —  Polarization 
before  attraction.  — Illustration. 

92.  Description   of  the   Holtz   machine.  —  Its    action. — 
The  explanation. 

93.  The  Leyden-jar.  — Various  forms.  — May  be  charged. 

—  May  be  discharged.  —  Battery. 

94.  Electricity  of  the    atmosphere.  —  Same    as   fractional 
electricity.  — Lightning. 

95.  Effect  of  points.  —  Lightning-rods. 

96.  Mechanical  effects  of  electricity. — Chemical. — Phys- 
iological. 

97.  Magnets.  — Experiment.  — Poles. 

98.  Attraction  and  repulsion. 

99.  Magnetic    polarization.  —  In    series.  —  Among    the 
molecules. 

100.  A  bar-magnet  supported. — Points  north  and  south. 

—  Its  variation.  — Annual  and  daily  changes. 

101.  Dip  of  the  needle. 

102.  Different   names   for  current   electricit}*. — Chemical 
action. — With    pure   zinc. — The   simple    cell. — Chemical 
action  in  simple  cell.  —  Electric  conditions   of  the    cell.  — 
Direction  of  the  current.  —  Enfeeblement  of  the  current.  — 
Remedied  in  Grove's  cell.  —  What  becomes  of  the  hydrogen? 

—  The  Bunsen  cell.  —  Other  forms. 

103.  Statement    of    Ohm's    law.  —  Definitions.  —  The 
formula.  — Units  of  C,  E,  and  R  (see  Review  Summary). 

104.  Battery  of  low  resistance.  — Its  electro-motive  force. 

—  Strength  of  current.  —  Batten*  of  high  resistance. — Its 
electro-motive   force. — The   resistance.  —  Strength  of  cur- 
rent. —  Quantity  and  intensit}T. 

105.  Electricity  produces  heat.  —  And  light. — And  mag- 
netism.—  The   electric  telegraph. — The   key. — The    line. 

—  The  register.  — Electricity  produces  chemical  action. 

106.  The  current  deflects  a  magnetic  needle.  — The  astatic 
needle.  — The  galvanometer. 

107.  Description  of  apparatus  for  induction  by  a  current. 


NATURAL   PHILOSOPHY.  273 

—  Results  of  experiment.  —  Induction  coils.  —  Ritchie's. — 
Experiment  with  a  magnet. — Magneto  electricit}'. — Simple 
form  of  machine.  — The  telephone.  — The  Bell  telephone.  — 
Its  action.  —  Edison's  carbon  transmitter.  —  The  micro- 
phone. 

108.  Thermo-electricity. 


274  NATUKAL   PHILOSOPHY. 


CHAPTER   IX. 
ON  MACHINERY. 


SECTION  I. 
ON  THE   SIMPLE  MACHINES, 

109.  THE  principle  of  work,  applied  to  any  one  of  the 
simple  machines,  will  determine  its  law  of  equilibrium. 

The  Principle  of  Work.  —  We  remember  that  work  is 
the  overcoming  of  resistance,  and  that  it  is  measured  by 
the  product  of  the  weight  by  the  vertical  height  through 
which  it  is  lifted.  The  principle  of  work  states  briefly  that 
two  forces^  acting  in  opposite  directions  upon  the  same  body, 
will  be  in  equilibrium  when  they  do  equal  amounts  of  work. 

Let  us  illustrate   a  single    case   by  means   of  Fig.    166. 
Suppose  two  bodies,  M  and  N,  hang  from  the  ends  of  a  bar, 
A  B,  which   rests  upon  the   point  C,  about  which   it   may 
-g      freely  turn.     If  it  does  turn,  and 
M   goes   up,   N  will  go  down, 
and  if  the  distance  B  C  is  twice 
the  distance  A  C,  then  N  will  go 


» M  ""     twice  as  far  as  M.     In  all  cases, 

Pig<  166<  the     vertical     heights     through 

which  the  two  bodies  will  move  have  the  same  ratio  as  their 
distances,  A  C  and  B  C,  from  the  center  of  motion.  These 
lines  may  then  be  used  instead  of  the  vertical  heights  in 
calculating  work.  Then  the  work  which  may  be  done  by  M 
will  be  M  x  A  C,  and  that  of  N  will  be  N  x  B  C.  Now, 
if  these  works  are  equal,  then  the  two  bodies  will  be  exert- 


NATURAL   PHILOSOPHY.  275 

ing  equal  forces  upon  the  bar  A  B,  and,  if  once  brought  to 
rest,  they  will  just  balance  each  other. 

Machines.  —  Machines  are  instruments  by  which  forces 
ma}*  be  applied  to  overcome  resistance,  or  do  work.  They 
are  so  made  that  a  small  force,  by  moving  rapidly,  may 
overcome  a  greater  resistance,  or  a  great  force,  by  moving 
slowly,  may  put  a  small  resistance  in  rapid  motion.  In 
all  cases  the  work  done  by  the  two  forces  must  be  equal. 

The  resistance  to  be  overcome  is  alwaj^s  called  the 
WEIGHT  :  the  force  which  overcomes  it  is  called  the  POWER. 

Simple  Machines.  —  There  are  six  simple  forms  of  ma- 
chines, usually  called  the  Mechanical  Powers.  Out  of  these 
six  simple  machines  all  forms  of  machinery,  complex  as  they 
may  be,  are  made.  We  name  them  in  the  order  which  is  to 
be  followed  in  describing  them. 

1.  The  Lever.  4.  The  Inclined  Plane. 

2.  The  Wheel  and  Axle.  5.  The  Wedge. 

3.  The  Pulley.  6.  The  Screw. 

The  Law  of  Equilibrium.  —  By  the  term,  law  of  equi- 
librium, is  meant  a  statement  of  the  relation  which  must 
exist  between  the  power  and  the  weight,  in  order  that,  when 
at  rest,  they  may  just  balance  each  other. 

110.  Levers  are  of  three  classes.  The  principle  of  mo- 
mentum, applied  to  the  lever,  shows  that  the  power  and 
weight  will  be  in  equilibrium  when  they  are  to  each  other 
inversely  as  the  perpendicular  distances  from  the  fulcrum  to 
the  directions  in  which  they  act.  A  compound  lever  acts  on 
the  same  principle.  Applications  of  the  lever  are  very 

numerous. 

F         A 


Levers.  —  A  lever  is  an 


inflexible  bar,  able  to  turn  Fig.  167t 

freely    upon     one    point. 

Thus,    if  the  line  A  B   (Fig.  167)  represents  an  inflexible 

bar,  resting   upon   some  support  at   F,  upon  which  it  has 


276  NATURAL   PHILOSOPHY. 

free  motion,  it  represents  a  lever.  The  point  F,  about 
which  the  lever  turns,  is  called  the  FULCRUM. 

Three  Classes  of  Levers.  —  That  point  of  a  lever  to 
which  the  power  is  applied  is  called  the  POINT  OF  APPLICA- 
TION. That  on  which  the  weight  acts  is  called  the  WORKING 

POINT.       Now,    the 

^          ^L. B    lever  takes  different 

•^  names   according  to 

the  relative  positions 

JL  w|j|  °f  the  point  of  ap- 

Fig.  168.  plication,  the  work- 

ing  point,    and    the 

fulcrum.  In  the  lever  represented  in  Fig.  168,  whose  ful- 
crum is  at  F,  a  power,  P,  acts  upon  one  end  of  the  lever,  A, 
while  a  weight,  W,  acts  upon  the  other,  B.  The  fulcrum 
is  between  the  point  of  application  and  the  working  point. 
This  is  called  a  lever  of  ihe  first  class. 

In  the  lever  (Fig.  169),  the  working  point,  B,  is  between 
the  point  of  application, 
A,  and  the  fulcrum,  E. 
This  is  a  lever  of  the 
second  class. 

In  the  lever  (Fig. 
170),  the  point  of  ap- 
plication, A,  is  between . 

the  working  point,  B,    ^ 
and    the    fulcrum,    F. 
This  is  a  lever  of  the 


.  »w 
third  class. 

All  levers  belong  to  Fig'  169' 

these  three  classes.  They  need  not,  however,  be  made  in 
the  simple  straight  form  shown  by  the  figures.  In  Fig.  171. 
the  line  A  F  B  represents  a  lever  whose  arms  make  a  right 
angle  at  the  fulcrum,  F.  It  is  a  lever  of  the  first  class  ;  so 
also  is  that  shown  in  Fig.  172  by  the  curved  line  A  F  B. 

Application  of  the  Principle  of  Work.  —  Now,  if  we 


NATURAL   PHILOSOPHY. 


277 


examine  the  figures  which  represent  the  three  classes  of 
lever,  we  see  that  in  each  one  the  power,  P,  and  the  weight, 
W,  are  two  forces  which  act  in  opposite  directions.  They 
will  be  able  to  just  balance  each  other,  when  of  such  strength 
that,  if  in  motion,  they  would  do  equal  amounts  of  work. 


w 


F 


w; 


Fig.  170. 


Fig.  171. 


The  lines  B  F  and  A  F  have  the  same  ratio  as  the  vertical 
heights  through  which  they  move  if  motion  occurs.  The 
work  of  the  power  is  therefore  P  x  A  F  ;  that  of  the  weight 
is  W  x  B  F.  If  equilibrium  takes  place  only  when  the 
amounts  of  work  are  equal,  then 

PxAF  =  WxBF;  hence, 
P  :  W  ::  B  F  :  A  F. 

This  proportion  teaches  us  that  the  power  and  weight  will 
be  in  equilibrium,  when  they  are  to  each  other  inversely  as 
the  distance  of  their  points  of  application  from  the  fulcrum. 

It  may  be,  however,  that  the  power  and  weight  do  not  act 
perpendicularly  upon  the  lever.  This  case  is  represented  by 
Fig.  172.  The  lever  A  B  has  its  fulcrum  at  F.  The  power, 
P,  and  the  weight,  W,  act  obliquely  at  B  and  A.  Now,  it 
is  evident  that  the  force  of  the  power,  acting  obliquely  at  B, 
is  not  all  expended  to  lower  the  lever,  but  that  if  it  were 
acting  upon  the  point  N,  perpendicularly,  it  would  exert  all 
its  forces  to  move  the  arm  N  F.  So  the  effect  of  the  weight 


278 


NATURAL   PHILOSOPHY. 


acting  obliquely  upon  A  will  be  the  same  as  if  it  were  acting 
perpendicularly  upon  an  arm,  M  F.  Hence  P  X  N  F  may 
be  taken  as  the  work  of  the  power,  and  W  x  M  F  as  the 
work  of  the  weight.  Putting  these  equal, 

PxNF  =  WxMF;  hence, 
P:  W  ::  M  F  :  N  F. 

Law   of  Equilibrium. — This    proportion    teaches   that 

the  power  and 
weight  will  be  in 
equilibrium,  when 
the  power  and 
weight  are  in- 
versely as  the  per- 
pendicular dis- 
tances from  the 
fulcrum  to  the  di- 
rections in  which 
they  act. 

This  principle 
is  called  the  LAW 
OF  EQUILIBRIUM 


Fig.  172. 

for  the  lever.     It  will  apply  to  all  possible  forms. 

The  Compound  Lever.  —  In   a  compound  lever  several 
simple  levers  are  generally  so  fixed,  that  the  short  arm  of 
one  may  act  upon  the  long  arm  of  another.     Fig.  173  shows 
a  compound  lever  made  up  of 
two  simple  levers  having  their 
fulcrums  at  F  and  F'. 

In  this  case  the  work  of  the 
power  will  be  equal  to  P  X  C  F 
X  B  F',  and  that  of  the  weight 
will  be  equal  to  W  x  D  F'  x 
A  F.  If  these  products  are  put 


D 

tP 

|F 

J 

4 

Fig.  173. 


into  the  form  of  an  equation  it  will  be  seen  that  the  power 
and  weight  will  be  in  equilibrium,  when  the  power  multiplied 
by  the  product  of  all  the  arms  on  its  side  of  the  fulcrum  is 


NATURAL  PHILOSOPHY.  279 

equal  to  the  weight  multiplied  by  the  product  of  all  the  arms 
on  its  side. 

The  compound  lever  is  used  when  it  is  not  convenient  to 
have  a  very  long  lever,  and  }*et  a  small  force  is  required  to 
sustain  a  very  large  weight.  If  the  long  arms  of  the  two 
simple  levers  be  six  and  eight  feet,  and  each  short  arm  is 
one  foot,  then  one  pound  power  at  C  wrill  balance  48  pounds 
at  D  ;  while  if  a  simple  lever  had  been  used  whose  long 
arm  was  as  long  as  those  two  long  ones  together,  6  +  8—14 
feet,  and  whose  short  arm  was  one  foot,  then  one  pound  at 
C  would  only  be  enough  to  balance  14  pounds  at  D. 

Applications  of  the  Lever Of  levers  of  the  first  kind 

man}'  familiar  examples  might  be  named.     The  hand-spike 

and  crow-bar  are  levers  of  this 

class.     Shears  and  pincers  are  _— —- —4t— - 

pairs  of  levers,  also  of  the  first      «(*«imiE^^ 

class ;    their  fulcrums  being  at       /  \  ^  A 

their  joints.  /    \  /     \ 

The    balance    is   one   of   the     / \ 

<3Lzmh> 

most  useful  applications  of  the 
lever.     Fig.    174    represents    a 

very  simple  form  of  this  instrument.  The  beam  a  b  is  a 
lever  poised  at  its  center,  the  pivot  or  fulcrum  c  being  a 
little  above  its  center  of  gravity.  From  the  ends  of  the 
beam  the  scale-pans  are  hung,  in  one  of  which  is  put  the 
body  to  be  weighed,  and,  in  the  other,  the  weights  to  balance 
it.  Balances  are  of  continual  use 
in  commerce  ;  the}*  are  indispensa- 
ble in  the  laboratory  of  the  chem- 
ist, for  whose  use  they  are  made 
with  so  great  skill  that  a  weight 
equal  to  the  y^i^  of  a  grain  can 
be  easily  weighed. 

The  steelyard  is  also  a  lever  of 
the    first    class,    but  with    unequal 
arms.      The   body  W,  Fig.   175,  to   be   weighed,    is   hung 


\ 


280  NATURAL   PHILOSOPHY. 

from  the  short  arm  of  the  lever  S  B,  and  it  is  balanced  by 
a  small  weight,  P.  It  is  clear  that  this  small  weight  will 
balance  more  weight  in  the  body  W,  as  it  is  moved  farther 
and  farther  from  the  fulcrum  C.  The  arm  B  C  has  notches 
cut  upon  it,  and  numbered,  to  denote  the  pounds  or  ounces 
in  W,  balanced  by  P,  when  at  these  points. 

Levers  of  the  second  class  are  not  so  common ;  the  wheel- 
barrow, however,  is  an  example  sufficiently  familiar.  The 
axle  of  the  wheel  is  the  fulcrum  ;  to  the  opposite  ends  of  the 
handles  the  power  is  applied,  while  the  load,  or  the  weight, 
rests  between  these  points.  The  oar  of  a  boat  is  a  lever  of 
this  kind,  where,  singular!}*  enough,  the  unstable  water 
^?1  serves  as  a  fulcrum  ;  the  hand  is  the  power  at  the  other  end 
of  the  lever,  while  the  boat  is  the  weight  between  them. 

Levers  of  the  third  class  are  often  met  with  in  the  arts. 
The  common  fire-tongs  and  the  sheep-shears  are  pairs  of 
levers  of  this  kind.  Their  fulcrums  are  at  one  end ;  the 
resistance  to  be  overcome  is  put  between  their  parts  near  the 
other  end,  while  the  fingers,  which  afford  the  power,  are  be- 
tween the  fulcrum  and  the  weight. 

Ill  The  wheel  and  axle  acts  on  the  principle  of  a  lever. 
The  power  and  weight  will  be  in  equilibrium  when  the  power 
is  to  the  weight  as  the  radius  of  the  axle  is  to  the  radius  of 
the  wheel. 

A  compound  wheel  and  axle  acts  on  the  same  principle  as 
a  compound  lever. 

One  wheel  may  be  made  to  turn  another  by  friction,  by 
cogs,  or  by  bands. 

Applications  of  this  machine  are  common  and  important. 

The  Wheel  and  Axle.  —  One  form  of  the  wheel  and 
axle  is  shown  in  Fig.  176.  It  consists  of  a  wheel,  B,  firmly 
fastened  to  an  axle,  A,  and  turning  freely  around  an  axis, 
one  end  of  which  is  shown  at  C.  The  power,  P.  acts  upon 
the  circumference  of  the  wheel,  and  the  weight,  "W,  acts 
upon  the  axle  by  means  of  a  rope  winding  around  it  in  the 
opposite  direction. 


NATURAL  PHILOSOPHY. 


281 


It  acts  on  the  Principle  of  the  Lever.  —  If  we  have 
an  end  view  of  the  machine,  it  will  be  seen,  as  shown  in 
Fig.  177,  where  the  large  circle  represents  the  wheel,  and 
the  small  circle  the  axle ;  the  center,  C,  being  the  end  of  the 
axis.  At  the  point  A,  the  power  acts  on  the  wheel,  and 
from  the  point  B,  on  the  other  side  of  the  center,  the 
weight  is  suspended.  Now.  if  a  straight  line,  A  B,  join  the 


Fig.  176. 


Fig.  177. 


points  A  and  B,  it  will  pass  through  the  center,  and  repre- 
sent a  lever,  whose  fulcrum  is  at  C.  It  is  upon  the  ends 
of  such  a  lever  that  the  power  and  weight  are  constantly 
acting. 

Application  of  the  Principle  of  Work.  —  The  work 
of  the  power  is  represented  by  P  x  AC;  that  of  the  weight 
by  W  x  B  C.  If  the  two  forces  are  able  to  balance  each 
other,  these  products  are  equal.  Hence, 

P  x  A  C  =  W  X  B  C  ;  or, 
P  :  W  ::  B  C  :  A  C. 

But,  in  the  figure,  we  notice  that  A  C  is  the  radius  of 
the  wheel,  and  that  B  C  is  the  radius  of  the  axle.  Then  the 
proportion  teaches  us  that  the  power  and  iveight  will  be  in 
equilibrium  when  the  power  is  to  the  weight  as  the  radius  of 
the  axle  is  to  the  radius  of  the  wheel. 

If  the  radius  of  the  axle  is  one  foot,  and  that  of  the  wheel 
three  feet,  then  one  pound  upon  the  wheel  will  balance  three 
pounds  upon  the  axle. 


282 


NATURAL  PHILOSOPHY. 


Fig.  178. 


The  Compound  Wheel  and  Axle.  —  When  more  thati 
one  wheel  and  axle  are  connected,  so  that  the  axle  of  each 
may  act  on  the  wheel  of  the  next,  the  machine  is  a  com- 
pound wheel  and  axle.  Such  an  arrangement  is  shown  in 
Fig.  178.  We  may  get  the  law  of  equilibrium  in  the  same 
way  as  in  the  compound  lever.  The  work  of  the  power  will 

be  P,  multiplied  by  the  several 
radii  of  the  wheels  ;  that  of  the 
weight  will  be  W,  multiplied  by 
the  several  radii  of  the  axles. 
If  the  two  forces  are  able  to 
balance  each  other,  these  values 
must  be  equal.  Hence  we  learn 
that  in  a  compound  wheel  and 
axle,  the  power  and  weight  will 
be  in  equilibrium,  when  the 
power  multiplied  by  the  product 
of  the  radii  of  the  wheels  equals 
the  weight  multiplied  by  the  product  of  the  radii  of  the  axles. 

It  is  easy  to  see  that  in  this  way  a  small  power  may  be 
made  to  balance  a  much  larger  weight  than  it  could  by  acting 
upon  a  simple  wheel  and  axle,  unless  the  wheel  should  be  so 
large  as  to  be  unwield}'. 

One  Wheel  may  turn  another  by  means  of  Cogs. — 
In  Fig.  178,  there  may  be  seen  projecting  teeth  on  the 
circumferences  of  the  axles,  b  and  c,  which  fit  into  equal 
notches  on  the  circumferences  of  the  wheels.  Neither  the 
axles  nor  the  wheels  can  turn  without  causing  the  other  to 
turn  also.  This  is  the  common  and  convenient  method  of 
giving  motion  from  one  wheel  to  another.  The  wheels  of  a 
clock  are  cog-wheels  :  those  of  a  watch  also  beautifully  illus- 
trate this  mode  of  communicating  motion. 

By  Friction.  —  When  the  circumferences  of  the  wheels 
and  the  axles  are  made  smooth,  the}'  may  be  pressed  so 
snugly  together,  that  neither  can  turn  without  turning  the 
other  at  the  same  time,  in  the  opposite  direction.  In  this 


NATURAL   PHILOSOPHY.  283 

case,  the  motion  is  communicated  by  the  friction  of  the  parts 
against  each  other. 

By  Bands.  —  A  third  method  of  giving  motion  to  a 
train  of  wheel- work  consists  in  the  use  of  bands  or  belts, 
which  encircle  the  parts  which  are  to  act  upon  each  other. 
In  the  spinning-wheel,  for  example,  the  spindle  is  turned  b;y 
a  band  which  passes  around  it  and  the  axle  of  the  wheel- 
head.  Another  band  passes  around  the  wheel-head  and  the 
large  wheel,  which  is  turned  by  the  hand  of  the  spinner. 
From  the  horse-power  of  a  threshing-machine,  also,  motion 
is  given  to  the  C}Tlinder  by  means  of  a  belt. 

Applications  of  the  Wheel  and  Axle.  —  Many  forms 
of  the  wheel  and  axle  are  in  common  use :  the  windlass  is 
one  of  the  most  familiar,  being  often  used  to  raise  water 
from  wells.  One  form  of  the  windlass  is  represented  in  Fig. 
176.  A  crank  is  often  used  in  place  of  the  wheel,  B.  The 
common  grindstone  is  a  homely  illustration  of  the  wheel 
and  axle  :  the  crank  is  in  place  of  a  wheel ;  the  stone  itself 
is  the  axle.  The  power  is  the  force  of  the  hand,  while  the 
weight  is  the  resistance  offered  b}r  the  tool  pressing  on  the 
edge  of  the  stone. 

If  the  axle  is  in  a  vertical  position,  and  the  forces  of  power 
and  weight  act  horizontally,  the  machine  is  then  called  a  CAP- 
STAN, and  is  much  used  on  board  of  ships. 

The  compound  wheel  and  axle  is  used  in  almost  every  mill 
and  factory.  Two  objects  are  sought  in  its  use  :  either  great 
resistance  is  to  be  overcome,  or  rapid  motion  is  to  be  secured. 
To  overcome  great  resistances,  the  power  is  applied  to  the 
circumference  of  the  first  wheel  in  the  system,  and  the  weight 
is  acted  upon  by  the  last  axle.  This  case  is  shown  in  Fig. 
178.  To  secure  rapid  motion,  the  power  is  applied  to  the 
first  axle,  while  the  weight  is  acted  upon  by  the  circumference 
of  the  last  wheel.  The  same  figure  illustrates  this  case  also, 
if  we  will  suppose  the  heavy  body,  W,  to  act  as  a  power  to 
put  the  lighter  body,  P,  in  motion.  If  we  suppose  the  radius 
of  each  axle  to  be  one  foot,  and  of  each  wheel  ten  feet,  then 


284  NATURAL   PHILOSOPHY. 

P  x  10  x  10  x  10  =  W  x  1  X  1  X  1  ;  or,  1,000  P  =  W. 
Now,  W  being  1,000  times  heavier  than  P,  P  must  move 
1.000  times  faster  than  W.  In  this  way,  a  great  power 
ma}T  be  changed  into  rapid  motion.  An  example  of  this  is 
found  in  the  saw-mill,  where  the  slow  motion  of  a  heavy  body 
of  water,  acting  against  a  water-wheel,  is  given,  by  means 
of  cogs  and  belts,  from  wheel  to  wheel,  until  it  re-appears, 
multiplied  a  thousand-fold,  in  the  buzzing  saw. 

112.  The  pulley  may  be  either  fixed  or  movable.  In  the 
fixed  pulle}*  the  power  and  weight  will  be  in  equilibrium  when 
they  are  equal. 

In  the  movable  pulley,  with  a  single  rope,  the  power  and 
weight  will  be  in  equilibrium  when  the  power  is  equal  to  the 
weight,  divided  b}*  the  number  of  branches  of  rope  which 
sustains  the  weight. 

In  movable  pulleys,  with  separate  ropes,  the  power  and 
weight  will  be  in  equilibrium  when  the  power  equals  the 
weight,  divided  by  two  raised  to  a  power  shown  by  the 
number  of  pulleys. 

The  applications  of  the  pulley  are  common  and  important. 

The  Pulley.  —  A  pulley  is  a  grooved  wheel,  turning 
freely  about  its  axis,  with  a  rope  passing  over  or  around  it. 
It  is  shown  in  Fig.  179.  The  grooved  wheel,  A,  moves 
freely  upon  its  axis,  while  over  its  circumference  goes  the 
rope,  to  the  ends  of  which  the  power  and  the  weight  are 
fastened. 

Is  either  Fixed  or  Movable.  —  If  the  axis  of  the  pull- 
ey is  stationary  (see  Fig.  179),  the  pulley  is  called  a  FIXED 
PULLEY.  One  whose  axis  moves  with  the  weight  is  called  a 
MOVABLE  PULLEY.  This  will  be  understood  by  means  of 
Fig.  180.  The  wheel,  E,  is  a  movable  pulle}r.  From  its 
axis  the  weight  is  hung,  while  the  rope,  one  end  of  which  is 
fastened  to  a  fixed  support  at  D,  passes  under  it,  and  then 
over  a  fixed  pulley,  A.  The  power  is  applied  to  this  end  of 
the  rope. 


NATURAL   PHILOSOPHY. 


285 


The  Principle  of  Work  applied  to  the  Fixed  Pulley. 

—  The  fixed  pulle}'  is  shown  in  Fig.  179,  to  which  we  again 
refer.  It  is  clear  that,  when  motion  occurs,  the  power,  P. 
will  go  down  exactly  as  far  as  the  weight,  W,  goes  up. 
To  do  equal  work  when  the  distances  are  equal,  the  bodies 
must  have  equal  weights.  Hence,  in  the  fixed  pulley  the 
power  and  weight  can  balance  each  other  only  when  they  are- 
equal. 


pQ 


W 


Fig.  179. 


Fig.  180. 


The  Principle  of  Work  applied  to  the  Movable 
Pulley  with  a  single  Rope.  —  In  the  movable  pulley  with 
a  single  rope  (see  Fig.  180),  the  weight  rests  upon  two 
branches  of  the  rope,  H  and  E ;  and,  when  it  rises,  both 
branches  must  be  equally  shortened.  But  the  rope,  F  P,  will 
lengthen  just  as  much  as  both  the  branches  shorten.  It  is 
clear  that  the  power,  P,  must  move  down  just  twice  as  far 
as  the  weight,  W,  goes  up.  Let  V  represent  the  vertical 
height  through  which  the  power  moves,  then  ^  will  represent 
the  vertical  height  through  which  the  weight  is  lifted.  The 
work  of  P  will  be  represented  by  P  x  V,  and  that  of  W  by 
W  X  ^,  and  the  two  forces  will  balance  each  other  when 
P  X  V  =  W  X  |,  or  when  P  =  f . 


286 


NATURAL   PHILOSOPHY. 


Now  let  us  take  another  case.  Suppose  there  are  two 
movable  pulleys,  C  and  D  (Fig.  181),  with  a  single  rope, 
one  end  being  fastened  at  F,  while  to  the  other  end  the 
power,  P,  is  applied.  In  this  case  we  find  that 
the  weight  is  supported  by  four  branches  of  the 
rope,  and  we  see,  too,  that,  when  it  rises,  all 
four  of  these  branches  must  be  shortened  alike. 
But  the  rope,  E  P,  must  at  the  same  time 
lengthen,  as  much  as  all  the  branches  shorten, 
so  that  the  distance  of  P  downward  must  be 
four  times  as  great  as  that  of  W  upward. 
Then,  if  V  is  the  vertical  height  for  P,  J  will 
be  the  vertical  height  for  W  ;  and,  if  they  do 
equal  work, 

P  X  V  -  W  x  |,  or  P  =  f  . 
In  like  manner,  if  three  movable  pullej's  are 

used,  we  shall  find  that,  to  be  in  equilibrium, 
Pig.  181.        p  __  w 

If,  now,  we  notice  that  in  each  of  the  values  of  P  just 
found,  the  denominator  of  the  fraction  is  the  number  of 
branches  of  the  rope  which  supports  the  weight,  we  have 
this  general  principle :  in  movable  pulleys,  with  a  single 
rope,  the  power  and  weight  will  be  in  equilibrium  when  the 
power  equals  the  weight  divided  by  the  number  of  branches 
which  support  it. 

The  Movable  Pulley  with  separate  Ropes.  —  When 
each  pulley  has  a  separate  rope,  the  law  is  very  different. 
Fig.  182  shows  such  a  s}Tstem.  The  three  ropes,  d  fh,  are 
fastened  to  the  beam.  The  first,  after  passing  around  the 
pulley,  b  d,  is  fastened  to  the  axis  of  the  one  above  :  so 
the  rope  /,  after  going  around  the  pulley  e/,  is  fastened  to 
the  axis  of  g  h;  but  the  rope  7i,  after  going  under  the  pulley 
g  7i,  passes  over  a  fixed  pulle}',  and  receives  the  power  at  the 
other  end. 

The  Principle  of  Work  applied  to  the  Movable 
Pulley  with  separate  Ropes.  —  This  system  is  only  a 


NATURAL   PHILOSOPHY. 


287 


combination  of  movable  pulleys  with  a  single  rope.  Suppose 
the  pulleys  b  d  and  ef  were  taken  away,  the  weight  being 
hung  from  the  axis  of  g  li.  There  would  be  left  an  arrange- 
ment exactly  like  that  shown  in  Fig. 
180.  g  h  is  a  movable  pulley,  with  a 
single  rope,  to  lift  the  pulley  e  f,  which 
is  likewise  a  movable  pulley,  with  a 
single  rope,  to  lift  the  pulley  b  d;  while 
b  d  is  itself  a  movable  pulley,  with 
a  single  rope,  to  lift  the  weight,  W. 
The  effect  of  the  power,  P,  will  be 
doubled  by  each  pulley  thus  :  - 
With  1  pulley,  P  =  5  =  5  ; 
"  2  pulleys,  P  =  f  =  f, ; 
"  3  pulleys,  P  =  f  =  5,. 

If  we  notice  that  the  denominator, 
in  each  of  these  values  of  P,  is  a 
power  of  two,  whose  index  is  the  num- 
ber of  pulleys,  we  infer  that,  in  a  sj's- 
tem  of  movable  pulleys  with  separate 

ropes,  the  power  and  tveight  will  be  in  equilibrium  when  the 
poiver  equals  the  weight  divided  by  a  poiver  of  two,  whose 
index  is  the  number  of  pulleys. 

For  example,  with  a  system  of  five  pullej^s,  how  much 
weight  will  a  power  of  ten  pounds  balance  ? 

P  =  w  .  or  10  =,w  .  hence  w  =  320  pounds. 

Applications  of  the  Pulley.  —  No  mechanical  advan- 
tage is  gained  by  the  use  of  the  fixed  pulley,  because  the 
weight  must  move  just  as  fast  as  the  power,  }~et  it  is  of  great 
value  in  the  arts,  for  changing  the  direction  of  forces.  A 
sailor  standing  upon  the  deck  of  his  ship  ma}',  by  the  use 
of  a  fixed  pulle}*,  hoist  the  sail  to  the  top  of  the  loftiest 
mast ;  or  when  heavy  bales  or  boxes  are  to  be  lifted  to  the 
upper  floors  of  warehouses,  a  horse,  trotting  along  the  level 
yard  or  street  (Fig.  183),  will  lift  them  as  effectually  as 
though  he  were  able  to  climb  the  perpendicular  wall  with  the 
same  rapidity. 


288 


NATURAL   PHILOSOPHY. 


The  Movable  Pulleys  with  single  rope  are  in  common  use 
for  moving  heavy  weights   through  considerable   distances. 
Merchandise  may  be  lifted  by  means  of  them,  from  the  hold 
of  a  ship  to  the  wharf,  or  to   the   upper  stories   of  store- 
houses ;  or,  by  a  different  arrange- 
ment of  the  machine,  the  ship  itself 
may  be  drawn  from  the  water  for 
repairs.       In    practice,    the    fixed 
pulleys    of    a    system    are    placed 
side  by  side,  and  thus  form  what 
is   called   a   BLOCK  :    the   movable 
pulleys,  likewise  side  by  side,  form 
another  block.     By  this  means  the 
system  is  made  compact. 

In  all  pull's  there  is  a  loss  of 
power,  due  to  the  friction  of  the 
pulleys  in  the  blocks,  to  the  weight 
of  the  lower  block,  and  to  the  stiff- 
ness of  the  ropes  used ;  so  that 
the  weight,  actually  overcome  by 
a  given  power,  is  always  less  than 


Fig.  183. 

the  laws  of  equilibrium  would  afford. 


113.  The  principle  of  work  applied  to  the  inclined  plane 
shows  :  — 

1st,  That,  when  the  power  acts  parallel  to  the  length  of 
the  plane,  the  power  and  weight  will  be  in  equilibrium  when 
the  power  is  to  the  weight  as  the  height  of  the  plane  is  to 
its  length ; 

2d,  That,  when  the  power  acts  parallel  to  the  base  of  the 
plane,  the  power  and  weight  will  be  in  equilibrium  when 
the  power  is  to  the  weight  as  the  height  of  the  plane  is  to 
its  base. 

The  applications  of  this  machine  are  very  numerous. 

The  Inclined  Plane. — Any  plane,  hard  surface,  placed 
in  an  oblique  position,  may  be  used  as  an  inclined  plane.  In 


NATURAL   PHILOSOPHY.  289 

Fig.  184,  A  B  represents  an  inclined  plane.  The  distance 
B  C  is  the  height  of  the  plane,  and  A  C  is  its  base.  The 
weight,  W,  may  be  urged  up  the  plane  by  a  force  acting  par- 
allel to  A  B,  or  parallel  to  A  C,  or  at  any  angle  to  these. 
We  are  to  notice  the  first  two  cases  only. 

If  the  Power  acts  parallel  to  the  Length  of  the 
Plane.  —  In  the  figure  the  power,  P,  by  means  of  a  rope 
going  over  the  fixed  pulley,  D,  at  the  top  of  the  plane,  acts 
upon  the  weight,  W, 
in  a  direction  W  D, 
parallel  to  the  length, 
A  B,  of  the  plane.  ^^  ^^S 

Now,  a  force  which 
will  urge   the    weight 
from  A  to  B  is  lifting  ^ 
it    only   through    the 
vertical   height,  C  B.  Fig'  184' 

But,  while  the  weight  goes  from  A  to  B,  the  rope  passing 
over  the  pulley  will  let  the  power  down  a  distance  equal  to 
A  B,  in  the  same  time.  The  work  of  the  power  is,  therefore, 
represented  by  P  X  A  B ;  that  of  the  weight,  by  W  x  C  B. 
When  these  products  are  equal,  the  two  forces  will  be  able  to 
balance  each  other.  Thus  :  — 

PxAB  =  WxCB;  or 
P  :  W  ::  CB  :  A  B. 

This  proportion  teaches  us  that,  when  in  equilibrium,  the 
power  is  to  the  weight  as  the  height  of  the  plane  is  to  its 
length. 

If,  for  example,  the   height   C   B   is   four  feet,  and  the 
length  of  the  plane,  A  B,  is  sixteen  feet,  a  power  of  one 
pound  will  balance  a  weight  of  four  pounds.     For  — 
1  Ib.  :  4  Ibs.  ::  4  ft.  :  16  ft. 

If  the  Power  acts  parallel  to  the  Base  of  the 
Plane.  —  Let  A  B  (Fig.  185)  represent  a  plane  whose 
height  is  C  B,  and  whose  base  is  A  C.  The  power  acts 
upon  the  weight  by  means  of  a  cord  passing  over  the  pulley 


290 


NATURAL   PHILOSOPHY. 


Fig.  185. 


at  C,  in  a  direction  parallel  to  A  C.  To  move  the  weight 
from  A  to  B,  will  be  lifting  it  only  through  the  vertical 

height,  C  B.  If  the 
pulle}*,  C,  could  be 
raised  while  the  weight 
goes  up,  so  as  to  keep 
the  cord  parallel  to 
A  C,  then  the  cord, 
passing  over  the  pull- 
e}',  will  let  the  power 
down  a  distance  equal 
to  A  C.  The  work 
of  the  power  is,  there- 
fore, represented  by 
P  X  A  C,  and  that  of 
the  weight,  by  W  x 
C  B.  If  now  these 
products  are  equal,  the  power  and  weight  will  just  balance 
each  other.  Hence  — 

PxAC  =  WxBC;  or 
P  :  W  ::  BC  :  AC. 

From  this  proportion  we  learn  that,  when  the  power  acts 
parallel  to  the  base  of  the  plane,  the  power  and  iveight  will 
be  in  equilibrium  ivhen  the  power  is  to  the  weight  as  the  height 
of  the  plane  is  to  its  base. 

Thus,  if  the  height  of  the  plane  is  two  feet,  and  the  base 
is  ten  feet,  a  power  of  one  pound  will  balance  a  weight  of 
five  pounds.  For  1  Ib.  :  5  Ibs.  ::  2  ft.  :  10  ft. 

Applications  of  the  Inclined  Plane.  —  This  machine 
is  used  to  lift  heavy  weights  through  short  distances.  Many 
familiar  examples  might  be  named.  If  a  barrel  of  mer- 
chandise is  to  be  placed  upon  a  wagon,  it  is  often  rolled  up 
on  a  plank,  one  end  of  which  rests  on  the  ground,  the  other 
on  the  wagon.  A  hogshead  which  a  dozen  men  could  not 
lift  may  thus  be  raised  by  the  strength  of  one  or  two. 

Our  common  stairs  are,  in  principle,  inclined  planes,  the 


NATURAL  PHILOSOPHY. 

arrangement  of  steps  only  giving  a  firm  footing.  If  the  dis- 
tance between  the  floors  be  three-fourths  the  length  of  the 
stairs,  then,  besides  the  ordinary  effort  of  walking,  the  per- 
son must  continually,  while  going  up,  labor  to  lift  three- 
fourths  of  the  weight  of  his  body. 

114.  The  wedge,  in  its  most  common  form,  is  made  up 
of  two  inclined  planes  joined  together  at  their  bases.     The 
sharper  the  wedge,  the  greater  the  resistance  which  may  be 
overcome  by  it. 

The  Wedge.  —  This  instrument  is  shown  in  use  b}'  Fig. 
186.  A  B  is  called  the  back  of  the  wedge:  A  c  and  B  c 
are  its  sides,  and  c  is  its  edge. 
It  is  generally  used  in  cleaving 
timber,  and  sometimes  for  raising 
heavy  weights  through  very  short 
distances.  For  these  purposes  its 
edge  is  put  into  a  crevice  made  for 
it,  and  it  is  then  driven  by  blows  Pig. 

with  a  sledge. 

Since  we  can  not  calculate  the  force  of  a  blow,  no  attempt 
is  here  made  to  establish  a  law  of  equilibrium  for  the  wedge. 

115.  This  principle  applied  to  the  screw  shows  that :  — 
The   power  and  weight  will  be   in  equilibrium  when  the 

power  is  to  the  weight  as  the  distance  between  two  con- 
tiguous threads  is  to  the  circumference  of  the  circle  in  which 
the  power  moves. 

The  screw  is  used  extensively  to  produce  great  pressure. 
It  is  also  often  used  to  measure  delicate  distances. 

The  Screw.  —  The  screw  consists  of  a  cylinder  of  wood 
or  metal,  with  a  spiral  groove  winding  around  its  circumfer- 
ence. This  grooved  cylinder  (C,  Fig.  187)  passes  through 
a  block,  N  G,  on  the  inside  surface  of  which  is  a  spiral 
groove,  into  which  the  raised  parts  of  the  cylinder  exactly 
fit.  The  block  is  usually  called  the  nut.  The  raised  part 
between  the  grooves  of  the  cylinder  is  called  the  thread. 


292 


NATURAL  PHILOSOPHY. 


Suppose  the  nut  to  be  stationary :  then,  n  the  screw  is 
turned  by  a  power  acting  upon  the  lever  at  B,  it  must  ad- 
vance downward  at  every  revolution,  and  the  pressure  of  the 

advancing  screw  will  be  ex- 
erted upon  an}T  object  placed 
under  the  press-board,  E  F, 
against  which  the  end  of  the 
screw  presses. 

Application  of  the 
Principle  of  Work.  — By 
one  turn  of  the  screw,  it 
will  advance  downward  a 
distance  just  equal  to  the 
distance  between  two  con- 
tiguous threads.  The  press- 
board,  E  F,  which  may  be 
regarded  as  the  weight,  will 
be  moved  along  through  an 
equal  distance,  a  6,  by 
every  turn.  The  power  act- 
ing at  B  will,  in  the  same 
time,  move  through  the  circumference  of  the  circle  whose 
radius  is  B  C.  Hence  the  work  of  the  power  will  be  repre- 
sented by  P  x  circumference  of  the  circle  whose  radius  is 
B  C,  and  that  of  the  weight  by  W  X  a  b.  If  these  products 
are  equal,  the  two  forces,  when  at  rest,  will  be  in  equilibrium. 
Hence :  — 

P  x  circ.  B  C  =  W  x  a  6;  or 
P:  W  ::ab  :  circ.  B  C. 

This  proportion  teaches  that  the  power  and  weight  will  be 
in  equilibrium  ivhen  the  power  is  to  the  weight  as  the  distance 
between  two  contiguous  threads  is  to  the  circumference  of  the 
circle  in  which  the  power  moves. 

Thus,  if  the  distance  between  the  threads  is  \  inch,  and 
the  circumference  traveled  by  the  power  is  5  feet,  or  60 
inches,  what  weight  on  the  nut  would  one  pound  power  at 
B  balance? 


Pig.  187. 


NATURAL  PHILOSOPHY.  293 

1  Ih.  :  W  ::  1  in.  :  60  in.  W  =  120  Ibs. 

Applications  of  the  Screw.  —  The  screw  is  used  when 
great  weights  are  to  be  lifted  short  distances,  or  when 
heav}*  pressure  is  to  be  exerted.  By  its  use,  cotton  is 
pressed  into  bales,  the  juices  of  fruits  extracted,  and  oils 
pressed  from  vegetable  bodies  such  as  linseed  and  the 
almond . 

Micrometers.  —  In  contrast  with  these  uses  of  the  screw, 
depending  on  the  immense  pressure  it  can  exert,  is  another, 
remarkable  for  its  delicacy.  It  is  used  to  measure  very 
small  distances  when  accuracy  is  required.  Screws  with 
threads  of  exceeding  fineness,  and  called  MICROMETERS,  are 
used  for  this  purpose.  Suppose  a  screw  with  a  hundred 
threads  in  one  inch  of  its  length  ;  then,  at  every  turn  its  end 
would  advance  just  jfa  of  an  inch,  and,  if  it  carry  a  steel 
marker,  spaces  of  that  length  may  be  marked  off  on  any 
body  alongside  of  which  it  moves.  Now,  let  the  power 
move  in  a  circle  ten  inches  in  circumference,  and  let  this 
circle  be  graduated  to  inches,  tenths,  and  hundredths.  If 
the  power  move  one  inch  on  this  scale,  the  marker  on  the 
end  of  the  screw  will  go  forward  only  ^^  of  an  inch.  If 
the  power  goes  ^  inch,  then  the  marker  will  advance  only 
Tffj-<j-0  of  an  inch,  a  distance  quite  too  small  to  be  seen  ex- 
cept by  the  aid  of  a  good  microscope.  Astronomers  use 
the  micrometer  screw,  to  measure  the  apparent  sizes  of  the 
heavenly  bodies. 

SECTION   II. 

ON  WATER-POWER. 

116.  Water- wheels  are  turned  by  the  power  of  moving 
water.  There  are  several  kinds  :  first,  the  Undershot  wheel : 
second,  the  Overshot  wheel ;  third,  the  Breast  wheel ;  fourth, 
the  Turbine  wheel. 

The  Undershot  Wheel.  —  The  undershot  wheel  is  shown 
\n  Fig.  188.  Its  circumference  is  provided  with  float- 


•294 


1<TAT  tJH AL  PH I LOSOPH  Y". 


boards,  a  d  c,  against  which  the  running  water  acts.     Other 

wheels  are  connected  with  the  axle  of  this  one  b3*  cogs  and 

bands.     This  form  of  wheel  is  often  placed  in  a  horizontal 

position,  and  water  from  the 
bottom  of  a  dam  guided 
against  the  float-boards  of 
one  side. 

The  Overshot  Wheel. 
—  The  overshot  wheel  (Fig. 
189)  differs  from  the  under- 
shot, by  having  buckets 
upon  its  circumference,  in- 
stead of  float-boards.  The 
water  enters  the  buckets  at 
the  top  of  the  wheel,  and, 
filling  those  on  one  side  of 

it,  turns  the  wheel  by  its  weight.     The  buckets  all  open  in 

the  same  direction,  so  that  while  those  on  one  side  of  the 

wheel  are  full,  those  on  the  other  side  will  be  bottom  upward 

and  empty. 

The  Breast  Wheel. 

—  The     breast     wheel 

(Fig.  190)  differs  from 

the     undershot     wheel 

only  b}'  being  so  placed 

in  front  of  a  dam,  that 

the  water  shall  fall  upon 

the  float-boards  of  its 

circumference  on  a  level 

with  its  axis. 


Pig.  188. 


The  American  Tur- 
bine.  —  The  construc- 
tion of  the  turbine  is 


Pig.  189. 


more  complex  than  that  of  the  wheels  just  described.     Its 
action  may  be  understood  by  a  careful  study  of  Fig.  191. 
The  figure  shows  a  section  of  the  interior  of  the  wheel,  as 


NATURAL   PHILOSOPHY. 


295 


it  would  appear  to  one  who  looks  down  upon  it  as  it  lies  in 
its  horizontal  position.  In  the  center  is  a  circular  disk  of 
cast  iron,  A  B,  in  a  horizontal  position.  On  the  upper  sur- 
face of  this  disk  are 
fastened  the  curved 
guides,  a  a  a.  This 
disk  is  stationary. 
The  wheel  proper, 
C  D,  revolves  outside 
of  this  disk.  It  con- 
sists of  two  cast-iron 
plates,  one  above  the 
other,  the  space  be- 
tween them  being  di- 
vided into  numerous 


ra: 


Fig.  190. 


channels  bv  the  curved  partitions,  c  c  c.  The  partitions 
in  the  wheel,  and  the  guides  on  the  disk,  are  curved  in 
opposite  directions.  To  the  bottom  of  this  wheel  is  fastened 

a  cast-iron  plate,  which  ex- 
tends under  the  central  disk, 
A  B,  and  to  the  center  of 
this  plate  is  attached  a  ver- 
tical shaft  which  comes  up 
through  the  disk  at  E. 
The  revolving  part,  there- 
fore, consists  of  the  outside 
wheel,  D,  the  iron  plate  un- 
derneath, and  the  vertical! 
shaft,  E. 

The  turbine  is  placed  at, 
the  bottom  of  a  column  of 
water.  The  weight  of  the 
water  above  the  disk  forces  the  water  with  great  power  out 
from  between  the  curved  guides,  a  a,  into  the  curved  chan- 
nels, c  c,  of  the  wheel.  The  energy  of  these  streams  turns 
the  wheel  in  the  direction  in  which  they  strike  against  its 


Fig.  191. 


296  NATURAL   PHILOSOPHY. 

partitions.  The  vertical  shaft  turns  with  the  wheel,  and, 
by  means  of  cogs,  gives  motion  to  other  parts  of  the  ma- 
chinery. 

Of  all  forms  of  water-wheel,  the  turbine  is  most  energetic 
and  economical. 

SECTION   III. 

ON  THE   STEAM-ENGINE. 

117.  The  elastic  force  of  steam  is  applied  to  mechanical 
purposes  by  means  of  a  steam-engine.  The  essential  parts 
of  this  machine  are,  1st,  the  boiler  in  which  steam  is  gen- 
erated ;  2d,  the  cylinder  in  which  the  steam  is  made  to  move 
a  piston  ;  3d,  the  crank  b}*  which  the  piston  turns  a  wheel. 
Engines  are  either  high-pressure  or  low-pressure. 

The  Tension  of  Steam When  steam  is  formed  at   a 

temperature  of  212°,  its  elastic  force  or  tension  is  just  equal 
to  the  pressure  of  the  atmosphere,  or  15  pounds  to  the 
square  inch.  If  taken  out  into  another  vessel,  preserving 
its  temperature  and  denskvv,  it  will  exert  a  pressure  of 
15  pounds  to  the  inch.  By  subjecting  water  to  a  greater 
pressure,  its  boiling  point  is  raised,  and  the  elastic  force 
of  the  steam  is  increased.  The  Marcet's  globe  illus- 
trates this  principle.  It  consists  of  a  metallic  globe  (Fig. 
192),  which  is  furnished  with  a  long  glass  tube  and  scale, 
T,  a  stopcock,  S,  and  a  thermometer,  A,  whose  bulb  is 
inside  the  globe.  In  the  bottom  of  the  globe  is  a  little 
mercury,  into  which  the  end  of  the  tube,  T,  dips,  and  above 
the  mercury  is  a  quantit}T  of  water.  The  water  is  boiled 
until  the  air  is  driven  out  of  the  open  stop-cock.  At  this 
moment,  the  elastic  force  of  the  steam  is  just  15  pounds  to 
the  inch.  The  stop- cock  is  now  closed  :  the  thermometer 
at  once  shows  a  rise  of  temperature,  and  at  the  same  time 
the  mercury  begins  to  rise  in  the  tube,  showing  an  increase 
in  the  force  of  the  steam.  When  the  temperature  of  the 


NATURAL   PHILOSOPHY. 


297 


boiling  water  has  reached  249.5°,  the  expansive  force  of  the 
steam  is  equal  to  two  atmospheres,  or  30  pounds,  to  the  inch, 
and  at  306°  it  is  five  atmospheres,  or  75  pounds  to  the 
inch. 

If,  now,  this  elastic  force  of  steam  can 
be  made  to  act  alternately  upon  opposite 
sides  of  a  piston,  it  will  push  it  back  and 
forth,  from  one  end  of  a  cylinder  to  the 
other,  with  power  enough  to  move  any 
amount  of  other  machinery.  This  is  ac- 
complished in  the  steam-engine. 

The  Boiler.  —  The  boiler  of  a  steam- 
engine  is  usually  made  of  plates  of  wrought 
iron  riveted  together  in  the  form  of  a  c}*lm- 
der.  In  the  best  forms,  there  are  tubes 
which  run  lengthwise  through  the  body  of 
the  boiler,  through  which  the  flame  and  hot 
gases  from  the  fire  ma}*  pass.  The  water 
in  the  boiler  surrounds  these  tubes,  and  is 
rapidty  heated  by  them.  The  steam  thus 
formed  in  the  boiler  collects  above  the 
water,  and  by  its  pressure  raises  the  boiling 
point,  until,  when  its  elastic  force  is  suf- 
ficiently great,  the  steam  is  allowed  to  pass  through  a  pipe 
to  the  cjiinder. 

The  Cylinder.  —  The  arrangement  of  the  cylinder  and 
piston  are  shown  in  Fig.  193.  The  pipe  which  brings  the 
steam  from  the  boiler  enters  a  box,  d,  from  which  two 
tubes  lead,  one  to  the  top,  the  other  to  the  bottom  of  the 
metallic  c}'linder,  C,  in  which  the  piston,  P,  moves.  An- 
other tube  leads  from  this  box  out  into  the  air,  or  away  to 
another  vessel,  where  the  steam,  after  having  moved  the 
piston,  may  be  condensed.  A  sliding  valve,  ?/,  is  so  ar- 
ranged in  the  box  as  to  always  close  one  of  the  pipes  leading 
to  the  cylinder,  and  leave  the  other  open.  If  the  upper  tube 
is  open,  as  represented  in  the  figure,  the  steam  will  enter 


Fig.  192. 


298 


NATURAL  PHILOSOPHY. 


above  the  piston,  and  push  it  to  the  bottom  of  the  cylinder ; 
if  the  lower  tube  is  open,  the  steam  will  enter  below  the 
piston,  and  push  it  to  the  top.  In  either  case  the  steam  on 
the  opposite  side  of  the  piston  will  be  pushed  out  of  the 

C3'linder,  through  the  other  tube 
and  the  pipe,  O,  leading  from  the 
cavity  under  the  sliding  valve. 
When  the  steam,  entering  through 
the  lower  tube,  has  pushed  the 
piston  to  the  top  of  the  cylinder, 
the  valve  is  pushed  down  to  cover 
the  end  of  that  tube,  leaving  the 
end  of  the  other  uncovered,  so 
that  the  steam  may  pass  through 
it  to  act  above  the  piston.  By 
this  means  the  piston  will  be 
alternately  pushed  back  and  forth 
from  one  end  of  the  cylinder  to 
the  other. 

The  Crank.  —  By  this  simple 
motion,  back  and  forth,  the  piston 
turns  a  wheel  by  means  of  a 
crank.  To  the  piston-rod,  A 
(Fig.  193),  another  rod  is  joined  by  a  hinge ;  the  other  end 
of  this  rod  turns  a  wheel,  from  which  motion  may  be  com- 
municated to  others  by  bands  or  cogs. 

Besides  these  three  important  parts  of  the  steam-engine, 
there  are  numerous  other  appendages  for  particular  purposes, 
such  as  a  safety-valve  attached  to  the  boiler  to  regulate  the 
pressure  of  steam  in  it ;  the  governor,  to  regulate  the  supply 
of  steam  to  the  cylinder ;  the  fly-wheel,  a  heavy  wheel 
whose  inertia  causes  the  motion  of  the  machine^  to  be 
steady. 

Explain  Fig.  194.  —  The  picture   (Fig.  194)  shows  how 
the  piston-rod  gives  motion  to  machinery  in  another  way. 
In  the  first  place,  at  the  left,  we   see  the  cylinder  with 


Fig.  193. 


NATURAL   PHILOSOPHY. 


299 


one  side  cut  away,  so  as  to  expose  the  piston,  P,  inside. 
The  steam  is  supposed  to  be  entering  the  valve-box  at  S, 
and  to  be  going  to  the  upper  part  of  the  cylinder,  where  it 
is  pushing  the  piston  down. 

Next  we  observe  that  the  piston-rod,  A  D,  is  fastened  to 
one  end  of  the  large  and  strong  lever,  H  K.  As  the  piston 
goes  down  it  pulls  this  end  of  the  lever  down,  and  throws 


Pig.  194. 

the  other  end,  K,  up.  When  the  piston  rises  in  the  cylinder 
the  piston-rod  pushes  the  lever  end,  H,  up,  and  throws  the 
other  end,  K,  down.  Now,  as  the  lever  at  K  goes  up  and 
down,  it  pulls  and  pushes  upon  the  strong  arm,  J,  and  in  this 
way  turns  the  crank,  C.  The  large  wheel,  W  W,  fixed  upon 
the  axle,  will  thus  be  put  in  motion. 

Where  may  we  find  Engines  of  this  Form  ?  —  This 
form  of  engine  is  often  used  on  steamboats.     The  great 


300  NATURAL    PHILOSOPHY. 

lever,  UK,  ma}*  be  seen  above  decks  moving  alternately  up 
and  down  when  the  steamer  is  in  motion.  It  is  called  the 
"walking-beam."  The  strong  arm.  J,  reaches  down  into 
the  boat,  and  turns  an  enormous  iron  axle,  which  reaches 
quite  through  the  boat  from  side  to  side,  and  has  a  paddle- 
wheel  at  each  end. 

High  and  Low  Pressure  Engines.  —  The  different 
forms  of  steam-engines  are  almost  as  numerous  as  the 
machinists  who  make  them,  or  as  the  variety  of  purposes 
to  which  the}7"  are  applied.  There  are,  however,  two 
general  classes,  the  high^ressure  and  the  low-pressure 
engines. 

In  the  high-pressure  engines  the  steam,  after  moving  the 
piston,  is  thrown  out  from  the  cylinder  into  the  air.  In  the 
low-pressure  engines,  the  steam,  after  moving  the  piston,  is 
taken  off  to  a  vessel  called  the  condenser,  in  which  it  is 
changed  into  water.  The  first  is  called  high  pressure,  be- 
cause the  steam  which  moves  the  piston  must  push  the  steam 
from  before  the  piston  out  into  the  air,  which  presses  it  back 
with  a  force  of  15  pounds  to  the  inch.  To  do  this  evi- 
dently requires  a  pressure  of  15  pounds  to  the  inch  higher 
than  in  the  other  class,  in  which  the  steam  escapes  into 
a  vacuum,  and  can,  of  course,  exert  no  pressure  against  the 
piston. 

SECTION   IV. 

REVIEW. 
I.  —  SUMMARY   OP    PRINCIPLES. 

Two  forces,  in  opposite  directions,  will  be  in  equilibrium 
when  the}7  do  equal  amounts  of  work.  And  work  is  measured 
by  the  product  of  the  weight  of  the  body  moved  by  the 
vertical  height  through  which  it  is  lifted. 

Machines  are  instruments  with  which  forces  may  be  ap- 
plied to  do  work  to  better  advantage  than  if  they  were  to 
act  directly  upon  the  resistance  itself. 


NATURAL   PHILOSOPHY.  301 

The  Lever,  Wheel  and  Axle,  Pulley,  Inclined  Plane, 
Wedge,  and  Screw  are  the  simple  machines  out  of  which 
all  compound  machinery  is  made. 

The  power  applied  in  machinery  is  sometimes  moving 
water.  In  this  case  the  power  is  applied  b}'  means  of 
Water- Wheels. 

The  power  applied  is,  very  generally,  the  power  of  steam. 
In  this  case  it  is  applied  by  means  of  a  Steam-Engine. 

II.  — SUMMARY   OF  TOPICS. 

109.  The   principle   of  work. — Machines. — Simple  ma- 
chines. —  The  law  of  equilibrium. 

110.  Levers. — Three  classes. — Application  of  the  prin- 
ciple of  work.  —  Law  of  equilibrium.  — The  compound  lever. 

—  Applications  of  the  lever. 

111.  The  wheel  and  axle. — Acts  on  the  principle  of  the 
lever.  —  Application  of  the  principle  of  work. — The  com- 
pound wheel  and  axle.  —  Wheels  act  by  means  of  cogs.  — 
B}~  friction. — By  bands. — Applications  of  the  wheel  and 
axle. 

112.  The    pullc}*. — Fixed   and   movable. — Application 
of  the  principle  of  work  to  the  fixed  pulley.  — To  the  mova- 
ble pulley  with  one  rope.  — With  separate  ropes.  — Applica- 
tions of  the  pulley. 

113.  The  inclined  plane.  —  Power  parallel   to  the  length 
of  the  plane. — Power  parallel  to  the  base  of  the  plane. — 
Applications  of  the  inclined  plane. 

114.  The  wedge. 

115.  The  screw.  — Application  of  principle  of  work  to  the 
screw. — Applications  of  the  screw. — Micrometers. 

116.  The   undershot  water-wheel. — The  overshot  wheel. 

—  The  breast  wheel.  — The  turbine  wheel. 

117.  The  elastic  force  of  steam.  — The  boiler  of  a  steam- 
engine.  —  The  cylinder.  — The  crank.  — High  and  low  press- 
ure engines. 


302  NATURAL   PHILOSOPHY. 


III.  —  PROBLEMS. 

1.  If  a  power  of  10  pounds  act  upon  the  long  arm  of  a 
lever,  a  distance  from  the  fulcrum  of  6  feet,  what  weight 
would  it  balance  at  a  distance  of  2  feet  on  the  other  side  of 
the  fulcrum  ? 

Ans.  30  pounds. 

2.  In  a  lever  of  the  second  class,  the  power,  3  pounds,  is 
at  a  distance  of  one  foot   from   the   fulcrum :    what  weight 
will  it  balance  at  a  distance  of  one  inch  from  the  fulcrum  ? 

Ans.  36  pounds. 

3.  In  a  compound  lever,  the  long  arms  are  4  feet,  5  feet, 
and  6  feet  in  length ;  the  short  arms  are  1  foot,  2  feet,  and 
3  feet  long:  a  weight  of  2,000  pounds  is  to  be  balanced: 
how  much  power  must  act  upon  the  first  long  arm  ? 

Ans.  100  pounds. 

4.  A  power  of  10  pounds  lifts  a  weight  of  500  pounds  by 
means  of  a  lever  whose  short  arm  is   one   foot   long :  how 
long  is  the  long  arm  of  the  lever  ?  Ans.  50  feet. 

5.  If  the  500  pounds  in  the  last  example  is  to  be  lifted 
2  feet,  how  far  must  the  power  move  to  do  it? 

Ans.  100  feet. 

G.  The  radius  of  a  wheel  is  30  inches ;  of  its  axle,  5 
inches;  a  power  of  100  ounces  is  exerted  upon  the  wheel : 
how  much  weight  will  it  balance  at  the  axle  ? 

Ans.  600  ounces. 

7.  Three  wheels   and   axles  are  combined,  as   shown  in 
Fig.  1 78  ;  the  radius  of  each  wheel  is  20  inches ;  of  each 
axle,  is  4  inches  ;    a  power  of  2  pounds  acts   on  the  first 
wheel :  what  weight  will  it  balance  on  the  last  axle  ? 

Ans.  250  pounds. 

8.  A  force  of  16  pounds  is  applied  to  the  last  axle  (Fig. 
178) ,  and  moves  at  the  rate  of  10  inches  a  second  :  how  much 
weight  at  the  first  wheel  would  balance  it  at  rest?   and  how 
much  slower  will  it  go  when  in  motion  ? 

Ans.  .128  pound  ;   j^  as  fast. 


NATUKAL    PHILOSOPHY. 


303 


Fig.  195. 


9.  With  a  single   movable   pulley  a   stone  weighing   350 
pounds  is  to  be  lifted :  what  power  must  be  exerted  ? 

Ans.  1754-  pounds. 

10.  With  the  single  movable  pulley,  shown  in 
Fig.  195,  what  power  at  P  would  balance  a  weight 
of  250  pounds  at  W?  Ans.  83^  pounds. 

11.  If  the  weight,  W  (Fig.  195),  is  lifted  by 
the  power,  how  far  would  the  power  move  to  lift 
the  weight  one  foot?  Ans.  3  feet. 

12.  In  a  system  of  4  movable  pulleys,  with  a 
single  rope,  what    power   would   be   needed   to 
balance  a  weight  of  500  pounds  ? 

Ans.  62  J  pounds. 

13.  Suppose  each  of  the  4  pulle}*s  has  a  sepa- 
rate rope,  what  power  would  then  be  needed? 

Ans.  31  £  pounds. 

14.  An  inclined  plane,  6  feet  in  length  and  2  feet  high, 
is  used  to  put  a  barrel  of  flour  upon  a  cart.     The  barrel 
weighs  196  pounds:   how  much   force   must   a   man  exert, 
pushing  parallel  to  the  length  of  the  plane  ? 

Ans.  65  J+  pounds. 

15.  If  the  base  of  the  plane  were  5  feet,  its  height  2  feet, 
and  the  man  pushes  parallel  to  the  base,  how  much  force 
must  he  exert  to  lift  the  barrel  of  flour? 

Ans.  78f -f  pounds. 

16.  The  distance  between  the  threads  of  a  screw  is  one 
inch,  and  the  power  of  25  pounds  moves  in  a  circle  of  3  feet 
in  circumference  :  how  much  weight  will  it  balance  ? 

Ans.  900  pounds. 

17.  A  power  of  20  pounds,  by  means  of  a  screw,  exerts  a 
pressure    of  800  pounds.      The   threads    are  one-half  inch 
apart :  what  is  the  circumference  of  the  circle  in  which  the 
power  moves?  Ans.  20  inches. 


INDEX. 


(The  numbers  refer  to  pages.) 

Absolute  temperature 61 

Absolute  weight 48 

Acceleration 76 

Action  of  heat 135 

Adhesion  defined 13 

between  solids 13 

between  liquids  and  solids 14 

illustrated  by  experiment 13 

Air,  heated  by  convection 134 

undulations  in 106 

vibrations  of 102 

weighing  of ~ 36, 46 

Air-pump 45 

Air  thermometer 139 

Alcohol  thermometer 129 

Apparatus  for  induction 261 

Archimedes,  principle  of 34 

Armature 241 

Artesian  wells 30 

Ascent  of  a  balloon 48 

Astatic  needle 260 

Atmospheric  pressure 48 

shown  by  the  barometer 52 

depends  on  water-vapor 54 

Atmosphere,  pressure  of  one 51 

density  of 59 

Atom  defined 7 

Attraction 8,  16, 17 

Atwood's  machine 71 

Avogadro's  law 61 

Balance 279 

Balloon,  ascent  of 48 

Barometer 52 

305 


306  INDEX. 

Barometer,  corrections 53 

Forlin's 53 

predicts  changes  in  the  weather 54 

Bell,  vibrations  of 101 

Bell  telephone 265 

Black  lines  of  the  spectrum 198 

Boiling  point 142 

depends  on  pressure 143 

depends  on  purity  of  the  liquid 142 

depends  on  the  nature  of  the  vessel      ....  143 

expansion  at,  increases 144 

temperature  at,  constant         ......  144 

Boyle's  Law 57 

Breast-wheel 294 

Bright  lines  in  the  spectrum .        .  198 

Camera-obscura 214 

Capillarity 14 

familiar  examples  of 15 

illustrated  by  experiment 14 

law  of 15 

Center  of  gravity 81 

Centigrade  thermometer 138 

Central  forces 84 

Charles'  Law 60 

Chemical  action '.  259 

Chemism 15 

Cohesion 12 

Color  of  bodies 204 

depends  on  rapidity  of  vibrations 207 

of  clouds 205 

of  the  sky 204 

produced  by  interference  of  light 206 

Components 78 

in  a  given  direction   .                        79 

in  the  same  direction 80 

Composition  of  forces 77 

Compressibility  of  gases 44 

of  liquids 24 

Concave  lenses 193 

Concave  mirrors 175 

Conduction  of  heat ,        .,        .        .  132 

Conductivity 133 

Conductors 133 

Convection 134 

Convex  lenses «. 188 

Convex  mirrors 177 

Cords,  vibrations  of 98 


INDEX.  307 

Cords,  vibrations,  laws  of 97 

rate  of,  determined 99 

rate  invariable 101 

undulations  of 103 

Crystalline  form 23 

artificial 24 

in  nature 23 

Curved  motion 83 

Decomposition  of  light 195 

Diatonic  scale 155 

Dispersion  of  light 194 

Dispersive  power 196 

Diffusion  of  heat 200 

Diffraction  of  light 208 

Divisibility 6 

Double  refraction 216 

Ductility '      .          4,23 

Dynamic  theory  of  heat 126 

Echo 152 

Elasticity 3 

of  gase8 45 

of  liquids 24 

Electrical  machine,  frictional 225 

theHoltz 233 

Electric  units 270 

Electricity ~~r      .  224 

applied  to  registering  vibrations 99 

conductors  of 229 

current 247 

detected  by  electroscopes 227 

dynamic 247 

effects  of 240,  254 

electro-motive  force 230 

evolved  by  friction 224 

evolved  by  chemical  action 248 

evolved  by  induction 233,  261 

frictional  machine  for  producing 225 

Holtz  machine  for  producing 233 

induction 229,201,263 

insulation 230 

intensity  of 252,  254 

Ohm's  law 252 

polarization 230,  243 

potential 229 

quantity  of 254 

resistance  to 252 

strength  of  current 254 


308  INDEX. 

Electricity,  units  of 270 

Electro-chemical  telephone 265 

Electrolytes 259 

Electro-motive  force 230,  252 

Electroscopes 227 

Energy 114 

chemical 122 

conservation  of 123 

defined 118 

electrical 122 

kinetic 120 

measure  of 120 

mechanical 121 

molecular 121,  132 

of  the  sunbeam   .                        200 

potential 121 

radiant. 122,  169 

recognition  of,  by  the  senses 126 

relation  of,  to  mass  and  velocity 118 

relation  of,  to  work 119 

transmission  of 123 

transmutation  of 123 

undulatory 148 

varieties  of 121 

Ether 128 

Evaporation 142 

Expansibility  of  gases 44 

Expansion  of  gases  by  heat 137 

of  liquids 136 

of  solids 136 

temperature  measured  by 137 

Extension .1 

Eye,  description  of  the 214 

Fahrenheit's  thermometer 138 

Falling  bodies 71 

analysis  of  the  motion  of 74 

formulas  for     .        .        . 75 

laws  of 75 

Farad 271 

Foci 176 

Foot-pound 116 

Force 115 

attractive  or  repellant 8 

centripetal 84 

centrifugal 84 

constant 71 

impulsive 70 


INDEX.  309 

Force  in  solids,  liquids,  and  gases 20 

producing  motion 67 

Forces,  central 84 

composition  of 78 

molecular,  action  of 20 

of  nature 10 

resolution  of 79 

Fortin's  barometer 53 

Fulcrum 276 

Fundamental  ideas 16 

explain  the  three  forms  of  matter        ...  20 

explain  the  phenomena  of  motion        ...  67 

Galvanometer,  astatic 260 

Gases,  characteristic  properties  of 43 

expansion  of 44,  137 

kinetic  theory  of 51 

molecular  forces  in .20 

specific  gravity  of 36 

the  three  laws  of 57 

volume  of,  depends  on  pressure .58 

volume  of,  depends  on  temperature 60 

Glass,  ductility  of 4 

Gold,  malleability  of 4 

Gravitation 10 

laws  of 10 

not  limited  to  the  earth ' —  .12 

Gravity,  center  of 81 

specific 35 

Hardness 21 

Heat 132 

a  manifestation  of  energy 126 

conduction  of 132 

convection 134 

diffusion  of               200 

dynamic  theory  of 126 

effects  of 135 

evolved  by  blows 121 

evolved  by  chemical  energy 122 

evolved  by  electricity 254 

latent 139,  140 

mechanical  equivalent  of 124 

restoration  of 145 

sensible 139,  140 

specific 140 

Ice,  contraction  of,  by  heat 141 

Iceland  spar 216 

Impenetrability 2 


810  INDEX. 

Images 178 

by  concave  lenses 193 

by  concave  mirrors 180 

by  convex  lenses 190 

by  convex  mirrors 183 

by  plane  mirrors 179 

Inclined  plane 288 

applications  of 290 

Indestructibility 2 

Index  of  refraction 186 

Induction 229,230 

by  a  current  of  electricity 261 

by  a  magnet 263 

by  frictional  electricity 229 

coils 262 

Faraday's  theory  of 232 

Inertia 7 

Interference 104 

of  air-waves 108 

of  light         .                205 

of  sound 205 

of  water-waves 105 

Intervals  in  music 155 

Kinetic  energy 120 

Kinetic  theory  of  gases 51 

Latent  heat  of  water 142 

Law  of  Avogadro 61 

of  Boyle 57 

of  capillarity 15 

of  Charles 60 

of  conservation  of  energy 123 

of  electrical  attraction  and  repulsion 228 

of  electrical  induction     ....                ....  231 

of  gravitation 10 

of  intensity  of  light         .....'....  171 

of  equilibrium 275 

for  the  inclined  plane 289,  290 

for  the  lever 278 

for  the  pulley 286,287 

for  the  screw 292 

for  the  wedge 291 

for  the  wheel  and  axle 281 

of  magnetic  attraction  and  repulsion 242 

of  Marriotte 57 

of  Ohm .252 

of  reflection  of  light 172 

of  reflection  of  sound 152 


INDEX.  311 

Law  of  refraction  of  light 186 

of  transmission  of  light 169 

of  velocity  of  sound 148 

Laws  of  falling  bodies 75 

of  motion 67 

Lenses 187 

effect  of  concave 189 

effect  of  convex 188 

images  by 190 

Levers 275 

applications  of 279 

classes  of 276 

compound 278 

law  of  equilibrium 278 

principle  of  work  applied  to 276 

Light 169 

a  manifestation  of  energy 129 

an  undulatory  motion 128 

analogous  to  sound         .                                205 

definition  of .  129 

diffraction  of 208 

dispersion  of 194 

double  refraction  of 216 

intensity  of 171 

interference  of ^__    .  205 

polarization  of 217 

rays  of 169 

reflection  of 172 

refraction  of 184 

transmission  of 170 

velocity  of 170 

wave-lengths  of 206 

Line  of  direction 82 

Liquefaction 141 

Liquids,  characteristic  property  of         . 24 

convection  in 135 

compressibility  of 24 

elasticity  of 24 

expansion  of,  by  heat 136 

mobility  of 25 

molecular  forces  in    .        .        .        .        .        .        .        .         20, 25 

pressure  of 26 

specific  gravity  of 36 

Loadstone 241 

Luminous  bodies 128 

Machinery 274 

Machines .275 


312  INDEX. 

Magic-lantern 213 

Magnetic  needle 245 

astatic 260 

affected  by  a  current 260 

dip  of 247 

variations 246 

Magnetism 241 

Magneto-electricity 264 

Magneto-electric  machine 264 

Magneto-telephones 265 

Magnets 241 

Malleability 4 

of  metals 22 

Marriotte's  law  .                                57 

Mass 6 

distinguished  from  weight     .......       12, 114 

measure  of 113 

Measure  of  altitudes 54 

of  electric  current 270 

of  energy 118 

of  extension 2 

of  force 115 

of  mass 114 

of  wave-length 206 

of  work 116 

Mechanical  powers 275 

Melting  point 141 

Metals,  ductility  of 23 

Metric  measures x,  2 

Micrometers 293 

Microphone 268 

Microscopes 209 

Minute  division 6 

Mirrors 174 

Mobility  in  liquids 25 

in  gases 47 

Molecular  forces 20 

Molecule .  6 

Momentum 129 

Motion 67 

application  of  the  fundamental  ideas 67 

curved 83 

elements  of 69 

Newton's  laws  of 67 

of  air 90 

of  a  falling  body 71 

of  liquids .86 


INDEX.  313 

Motion  produced  by  a  single  force 67 

produced  by  two  or  more  forces 77 

uniform 69 

uniformly  accelerated 71 

Musical  flames 163 

Musical  instruments 161 

Musical  sounds 153 

intensity  of 157 

pitch  of 155 

quality  of 158 

Nature,  changes  of  condition  in 20 

crystalline  forms  in 23 

forces  of 10 

Natural  philosophy  denned 5,  17 

Newton's  rings 207 

Nodes  and  segments 105 

Ohm,  the 270 

Ohm's  law 252 

Opera-glass 211 

Optical  instruments •  209 

Organ-pipes 162 

Oscillation,  center  of        .        .        . 96 

Overshot  wheel 294 

Overtones 159 

Parallelogram  of  forces .        .^      .  77 

Pendulum,  described 93 

center  of  oscillation 96 

laws  of  the 93 

used  to  measure  time 97 

used  to  determine  the  form  of  the  earth    .        .  .97 

vibrations  of 94 

Phonograph 159 

Photometry 171 

Physics,  defined 5,  130 

Pitch  of  sound 155 

Polariscopes 218 

Polarization,  electrical 229 

of  the  battery 250 

of  light 216 

Potential,  electrical 229,  269 

Potential  energy 121 

Point  of  application 80 

Press,  hydrostatic 42 

Pressure,  a  unit  of 51 

equal  transmission  of,  by  water 41 

of  the  atmosphere 48 

of  liquids 26 


314  INDEX. 

Principle  of  stability 82 

Prisms 194 

Projectiles 85 

Properties,  chemical 4 

of  matter 1 

physical. 4 

Pulley,  applications  of 287 

classification 284 

principle  of  work  applied  to 285 

Pump,  air 45 

forcing 56 

suction 55 

Sprengel,  principle  of  the 90 

Radiometer 51 

Rainbow 202 

Range  or  random 85 

Reaumur's  thermometer 138 

Reflecting  telescopes 212 

Reflection  from  rough  surfaces 183 

of  sound 151 

of  light 172 

Refraction ,               184 

by  lenses 187 

by  prisms 194 

double 216 

index  of 186 

laws  of 185 

Refracting  telescopes 210 

Register,  the  electric .        .        .99 

Registering  vibrations 99 

Repulsion 8 

molecular 9 

Resolution  of  force 79 

Resultant  of  forces 78 

Ritchie's  induction  coil 262 

Ruhmkorff  coil 262 

Screw 291 

applications  of 293 

micrometer 293 

Sensitive  flames 165 

Siphon 56 

Siren 154 

Solids,  adhesion  between 13 

characteristic  properties  of 21 

expansion  of  by  heat 136 

loss  of  weight  of,  in  water 33 

no  convection  in  ...                135 


INDEX.  315 

Solids,  specific  gravity  of 38 

Sound 127 

compound 158 

distance  measured  by 151 

effect  of  temperature  on 151 

formula  for  velocity  of 151 

intensity  of 157 

laws  of  velocity  of 150 

musical 153 

pitch  of 155 

quality  of 158 

reflection  of 151 

transmission  of 149 

velocity  of .        .149 

waves 148 

Specific  gravity 35 

of  gases .        .  36 

of  liquids 36 

of  solids 38 

table  of 40 

Spectroscope 197 

Spectrum  analysis .        .199 

a  pure 197 

invisible  parts  of  a 199 

the  solar 196 

Springs -^       .  29 

Steam,  heating  by    . 145 

tension  of 296 

Steam-engine 297 

Steelyard 279 

Stereopticon 213 

Stringed  instruments 161 

Telephone,  Bell's 265 

Edison's 267 

Telescope 210 

astronomical 211 

Galileo's 211 

Herschellian 212 

terrestrial .        .212 

Temperature .        .  137 

absolute 61 

measured  by  expansion 137 

Tempering 22 

Tenacity 22 

Thermo-electricity 268 

Thermo-electric  pile 269 

Thermometers  .                                                                                       .  138 


316  INDEX. 

Thermometers,  relation  of  scales 146 

varieties  of 138 

Time  measured  by  the  pendulum 97 

Tone,  continuous 153 

Trade-winds 91 

Transmission  of  energy 123 

of  heat 201 

of  light 170 

of  sound 149 

Transmutation  of  energy 123 

Turbine  wheel 294 

Undershot  water-wheel 293 

Undulations       ..." 103 

denned 104 

in  air .        .        .        .106 

in  cords 103 

in  water 105 

period  of 104 

phase  of 104 

Undulatory  energy 148 

Uniformly  accelerated  motion 71 

Uniform  motion .        .        .69 

Unit  of  pressure 51 

of  work 116 

Units  in  electrical  measures 270 

Vacuum,  by  air-pump 45 

by  stream  of  water 90 

Vaporization 142 

Velocity  denned 69 

of  a  jet  of  water 86 

uniform 69 

uniformly  accelerated 71 

Vibration 92 

amplitude  of 94 

of  air 102 

of  a  bell .101 

of  cords  or  wires 97 

of  a  pendulum 93 

of  water 101 

phase  of 103 

producing  hearing 127 

rate  of  invariable 101 

registered  by  electricity 99 

transmission  of 103 

transverse  and  longitudinal .  108 

Vision 128 

Voice,  to  record  the 160 


INDEX.  317 

Voice,  to  reproduce  the 160 

Volt 271 

Water,  composition  of 7 

decomposition  of 259 

discharged  from  an  orifice 87 

latent  heat  of 142 

rising  in  pipes 28 

surface  of 27 

supply  to  cities 29 

vibrations  of 101 

Water-power 293 

Wave,  defined _ .  104 

front 169 

length 104,206 

period 104 

phase .104 

Waves  of  air .  106 

of  water 105 

interference  of 104 

Wedge 291 

Weighing  air 46 

Weight,  defined 11 

absolute 48 

distinguished  from  mass .        .        ,        .        .        .        .       12, 115 

laws  of 11 

not  confined  to  bodies  on  the  earth        .        .        .      ~7~~-  " .  12 

of  air 45 

the  resultant  of  parallel  forces 81 

Welding 13 

Wells,  artesian 30 

Wheelbarrow 280 

Wheel  and  axle 280 

acts  as  a  lever 281 

applications  of  the 283 

compound 282 

law  of  equilibrium .281 

turned  by  bands 283 

by  cogs 282 

by  friction .  282 

Wind 91 

Wind  instruments 162 

Work,  defined 116 

measure  of 116 

principle  of 274 


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